what problem solving methods

35 problem-solving techniques and methods for solving complex problems

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How do you identify problems?

How do you identify the right solution.

Tips for more effective problem-solving

Complete problem-solving methods

Problem-solving techniques to identify and analyze problems
Problem-solving techniques for developing solutions

Problem-solving warm-up activities

Closing activities for a problem-solving process.

Before you can move towards finding the right solution for a given problem, you first need to identify and define the problem you wish to solve.

Here, you want to clearly articulate what the problem is and allow your group to do the same. Remember that everyone in a group is likely to have differing perspectives and alignment is necessary in order to help the group move forward.

Identifying a problem accurately also requires that all members of a group are able to contribute their views in an open and safe manner. It can be scary for people to stand up and contribute, especially if the problems or challenges are emotive or personal in nature. Be sure to try and create a psychologically safe space for these kinds of discussions.

Remember that problem analysis and further discussion are also important. Not taking the time to fully analyze and discuss a challenge can result in the development of solutions that are not fit for purpose or do not address the underlying issue.

Successfully identifying and then analyzing a problem means facilitating a group through activities designed to help them clearly and honestly articulate their thoughts and produce usable insight.

With this data, you might then produce a problem statement that clearly describes the problem you wish to be addressed and also state the goal of any process you undertake to tackle this issue.

Finding solutions is the end goal of any process. Complex organizational challenges can only be solved with an appropriate solution but discovering them requires using the right problem-solving tool.

After you’ve explored a problem and discussed ideas, you need to help a team discuss and choose the right solution. Consensus tools and methods such as those below help a group explore possible solutions before then voting for the best. They’re a great way to tap into the collective intelligence of the group for great results!

Remember that the process is often iterative. Great problem solvers often roadtest a viable solution in a measured way to see what works too. While you might not get the right solution on your first try, the methods below help teams land on the most likely to succeed solution while also holding space for improvement.

Every effective problem solving process begins with an agenda . A well-structured workshop is one of the best methods for successfully guiding a group from exploring a problem to implementing a solution.

In SessionLab, it’s easy to go from an idea to a complete agenda . Start by dragging and dropping your core problem solving activities into place . Add timings, breaks and necessary materials before sharing your agenda with your colleagues.

The resulting agenda will be your guide to an effective and productive problem solving session that will also help you stay organized on the day!

Tips for more effective problem solving

Problem-solving activities are only one part of the puzzle. While a great method can help unlock your team’s ability to solve problems, without a thoughtful approach and strong facilitation the solutions may not be fit for purpose.

Let’s take a look at some problem-solving tips you can apply to any process to help it be a success!

Clearly define the problem

Jumping straight to solutions can be tempting, though without first clearly articulating a problem, the solution might not be the right one. Many of the problem-solving activities below include sections where the problem is explored and clearly defined before moving on.

This is a vital part of the problem-solving process and taking the time to fully define an issue can save time and effort later. A clear definition helps identify irrelevant information and it also ensures that your team sets off on the right track.

Don’t jump to conclusions

It’s easy for groups to exhibit cognitive bias or have preconceived ideas about both problems and potential solutions. Be sure to back up any problem statements or potential solutions with facts, research, and adequate forethought.

The best techniques ask participants to be methodical and challenge preconceived notions. Make sure you give the group enough time and space to collect relevant information and consider the problem in a new way. By approaching the process with a clear, rational mindset, you’ll often find that better solutions are more forthcoming.

Try different approaches

Problems come in all shapes and sizes and so too should the methods you use to solve them. If you find that one approach isn’t yielding results and your team isn’t finding different solutions, try mixing it up. You’ll be surprised at how using a new creative activity can unblock your team and generate great solutions.

Don’t take it personally

Depending on the nature of your team or organizational problems, it’s easy for conversations to get heated. While it’s good for participants to be engaged in the discussions, ensure that emotions don’t run too high and that blame isn’t thrown around while finding solutions.

You’re all in it together, and even if your team or area is seeing problems, that isn’t necessarily a disparagement of you personally. Using facilitation skills to manage group dynamics is one effective method of helping conversations be more constructive.

Get the right people in the room

Your problem-solving method is often only as effective as the group using it. Getting the right people on the job and managing the number of people present is important too!

If the group is too small, you may not get enough different perspectives to effectively solve a problem. If the group is too large, you can go round and round during the ideation stages.

Creating the right group makeup is also important in ensuring you have the necessary expertise and skillset to both identify and follow up on potential solutions. Carefully consider who to include at each stage to help ensure your problem-solving method is followed and positioned for success.

Document everything

The best solutions can take refinement, iteration, and reflection to come out. Get into a habit of documenting your process in order to keep all the learnings from the session and to allow ideas to mature and develop. Many of the methods below involve the creation of documents or shared resources. Be sure to keep and share these so everyone can benefit from the work done!

Bring a facilitator

Facilitation is all about making group processes easier. With a subject as potentially emotive and important as problem-solving, having an impartial third party in the form of a facilitator can make all the difference in finding great solutions and keeping the process moving. Consider bringing a facilitator to your problem-solving session to get better results and generate meaningful solutions!

Develop your problem-solving skills

It takes time and practice to be an effective problem solver. While some roles or participants might more naturally gravitate towards problem-solving, it can take development and planning to help everyone create better solutions.

You might develop a training program, run a problem-solving workshop or simply ask your team to practice using the techniques below. Check out our post on problem-solving skills to see how you and your group can develop the right mental process and be more resilient to issues too!

Design a great agenda

Workshops are a great format for solving problems. With the right approach, you can focus a group and help them find the solutions to their own problems. But designing a process can be time-consuming and finding the right activities can be difficult.

Check out our workshop planning guide to level-up your agenda design and start running more effective workshops. Need inspiration? Check out templates designed by expert facilitators to help you kickstart your process!

In this section, we’ll look at in-depth problem-solving methods that provide a complete end-to-end process for developing effective solutions. These will help guide your team from the discovery and definition of a problem through to delivering the right solution.

If you’re looking for an all-encompassing method or problem-solving model, these processes are a great place to start. They’ll ask your team to challenge preconceived ideas and adopt a mindset for solving problems more effectively.

Six Thinking Hats
Lightning Decision Jam
Problem Definition Process
Discovery & Action Dialogue

Design Sprint 2.0

Open Space Technology

1. Six Thinking Hats

Individual approaches to solving a problem can be very different based on what team or role an individual holds. It can be easy for existing biases or perspectives to find their way into the mix, or for internal politics to direct a conversation.

Six Thinking Hats is a classic method for identifying the problems that need to be solved and enables your team to consider them from different angles, whether that is by focusing on facts and data, creative solutions, or by considering why a particular solution might not work.

Like all problem-solving frameworks, Six Thinking Hats is effective at helping teams remove roadblocks from a conversation or discussion and come to terms with all the aspects necessary to solve complex problems.

2. Lightning Decision Jam

Featured courtesy of Jonathan Courtney of AJ&Smart Berlin, Lightning Decision Jam is one of those strategies that should be in every facilitation toolbox. Exploring problems and finding solutions is often creative in nature, though as with any creative process, there is the potential to lose focus and get lost.

Unstructured discussions might get you there in the end, but it’s much more effective to use a method that creates a clear process and team focus.

In Lightning Decision Jam, participants are invited to begin by writing challenges, concerns, or mistakes on post-its without discussing them before then being invited by the moderator to present them to the group.

From there, the team vote on which problems to solve and are guided through steps that will allow them to reframe those problems, create solutions and then decide what to execute on.

By deciding the problems that need to be solved as a team before moving on, this group process is great for ensuring the whole team is aligned and can take ownership over the next stages.

Lightning Decision Jam (LDJ) #action #decision making #problem solving #issue analysis #innovation #design #remote-friendly The problem with anything that requires creative thinking is that it’s easy to get lost—lose focus and fall into the trap of having useless, open-ended, unstructured discussions. Here’s the most effective solution I’ve found: Replace all open, unstructured discussion with a clear process. What to use this exercise for: Anything which requires a group of people to make decisions, solve problems or discuss challenges. It’s always good to frame an LDJ session with a broad topic, here are some examples: The conversion flow of our checkout Our internal design process How we organise events Keeping up with our competition Improving sales flow

3. Problem Definition Process

While problems can be complex, the problem-solving methods you use to identify and solve those problems can often be simple in design.

By taking the time to truly identify and define a problem before asking the group to reframe the challenge as an opportunity, this method is a great way to enable change.

Begin by identifying a focus question and exploring the ways in which it manifests before splitting into five teams who will each consider the problem using a different method: escape, reversal, exaggeration, distortion or wishful. Teams develop a problem objective and create ideas in line with their method before then feeding them back to the group.

This method is great for enabling in-depth discussions while also creating space for finding creative solutions too!

Problem Definition #problem solving #idea generation #creativity #online #remote-friendly A problem solving technique to define a problem, challenge or opportunity and to generate ideas.

4. The 5 Whys

Sometimes, a group needs to go further with their strategies and analyze the root cause at the heart of organizational issues. An RCA or root cause analysis is the process of identifying what is at the heart of business problems or recurring challenges.

The 5 Whys is a simple and effective method of helping a group go find the root cause of any problem or challenge and conduct analysis that will deliver results.

By beginning with the creation of a problem statement and going through five stages to refine it, The 5 Whys provides everything you need to truly discover the cause of an issue.

The 5 Whys #hyperisland #innovation This simple and powerful method is useful for getting to the core of a problem or challenge. As the title suggests, the group defines a problems, then asks the question “why” five times, often using the resulting explanation as a starting point for creative problem solving.

5. World Cafe

World Cafe is a simple but powerful facilitation technique to help bigger groups to focus their energy and attention on solving complex problems.

World Cafe enables this approach by creating a relaxed atmosphere where participants are able to self-organize and explore topics relevant and important to them which are themed around a central problem-solving purpose. Create the right atmosphere by modeling your space after a cafe and after guiding the group through the method, let them take the lead!

Making problem-solving a part of your organization’s culture in the long term can be a difficult undertaking. More approachable formats like World Cafe can be especially effective in bringing people unfamiliar with workshops into the fold.

World Cafe #hyperisland #innovation #issue analysis World Café is a simple yet powerful method, originated by Juanita Brown, for enabling meaningful conversations driven completely by participants and the topics that are relevant and important to them. Facilitators create a cafe-style space and provide simple guidelines. Participants then self-organize and explore a set of relevant topics or questions for conversation.

6. Discovery & Action Dialogue (DAD)

One of the best approaches is to create a safe space for a group to share and discover practices and behaviors that can help them find their own solutions.

With DAD, you can help a group choose which problems they wish to solve and which approaches they will take to do so. It’s great at helping remove resistance to change and can help get buy-in at every level too!

This process of enabling frontline ownership is great in ensuring follow-through and is one of the methods you will want in your toolbox as a facilitator.

Discovery & Action Dialogue (DAD) #idea generation #liberating structures #action #issue analysis #remote-friendly DADs make it easy for a group or community to discover practices and behaviors that enable some individuals (without access to special resources and facing the same constraints) to find better solutions than their peers to common problems. These are called positive deviant (PD) behaviors and practices. DADs make it possible for people in the group, unit, or community to discover by themselves these PD practices. DADs also create favorable conditions for stimulating participants’ creativity in spaces where they can feel safe to invent new and more effective practices. Resistance to change evaporates as participants are unleashed to choose freely which practices they will adopt or try and which problems they will tackle. DADs make it possible to achieve frontline ownership of solutions.

7. Design Sprint 2.0

Want to see how a team can solve big problems and move forward with prototyping and testing solutions in a few days? The Design Sprint 2.0 template from Jake Knapp, author of Sprint, is a complete agenda for a with proven results.

Developing the right agenda can involve difficult but necessary planning. Ensuring all the correct steps are followed can also be stressful or time-consuming depending on your level of experience.

Use this complete 4-day workshop template if you are finding there is no obvious solution to your challenge and want to focus your team around a specific problem that might require a shortcut to launching a minimum viable product or waiting for the organization-wide implementation of a solution.

8. Open space technology

Open space technology- developed by Harrison Owen – creates a space where large groups are invited to take ownership of their problem solving and lead individual sessions. Open space technology is a great format when you have a great deal of expertise and insight in the room and want to allow for different takes and approaches on a particular theme or problem you need to be solved.

Start by bringing your participants together to align around a central theme and focus their efforts. Explain the ground rules to help guide the problem-solving process and then invite members to identify any issue connecting to the central theme that they are interested in and are prepared to take responsibility for.

Once participants have decided on their approach to the core theme, they write their issue on a piece of paper, announce it to the group, pick a session time and place, and post the paper on the wall. As the wall fills up with sessions, the group is then invited to join the sessions that interest them the most and which they can contribute to, then you’re ready to begin!

Everyone joins the problem-solving group they’ve signed up to, record the discussion and if appropriate, findings can then be shared with the rest of the group afterward.

Open Space Technology #action plan #idea generation #problem solving #issue analysis #large group #online #remote-friendly Open Space is a methodology for large groups to create their agenda discerning important topics for discussion, suitable for conferences, community gatherings and whole system facilitation

Techniques to identify and analyze problems

Using a problem-solving method to help a team identify and analyze a problem can be a quick and effective addition to any workshop or meeting.

While further actions are always necessary, you can generate momentum and alignment easily, and these activities are a great place to get started.

We’ve put together this list of techniques to help you and your team with problem identification, analysis, and discussion that sets the foundation for developing effective solutions.

Let’s take a look!

The Creativity Dice
Fishbone Analysis
Problem Tree
SWOT Analysis
Agreement-Certainty Matrix
The Journalistic Six
LEGO Challenge
What, So What, Now What?
Journalists

Individual and group perspectives are incredibly important, but what happens if people are set in their minds and need a change of perspective in order to approach a problem more effectively?

Flip It is a method we love because it is both simple to understand and run, and allows groups to understand how their perspectives and biases are formed.

Participants in Flip It are first invited to consider concerns, issues, or problems from a perspective of fear and write them on a flip chart. Then, the group is asked to consider those same issues from a perspective of hope and flip their understanding.

No problem and solution is free from existing bias and by changing perspectives with Flip It, you can then develop a problem solving model quickly and effectively.

Flip It! #gamestorming #problem solving #action Often, a change in a problem or situation comes simply from a change in our perspectives. Flip It! is a quick game designed to show players that perspectives are made, not born.

10. The Creativity Dice

One of the most useful problem solving skills you can teach your team is of approaching challenges with creativity, flexibility, and openness. Games like The Creativity Dice allow teams to overcome the potential hurdle of too much linear thinking and approach the process with a sense of fun and speed.

In The Creativity Dice, participants are organized around a topic and roll a dice to determine what they will work on for a period of 3 minutes at a time. They might roll a 3 and work on investigating factual information on the chosen topic. They might roll a 1 and work on identifying the specific goals, standards, or criteria for the session.

Encouraging rapid work and iteration while asking participants to be flexible are great skills to cultivate. Having a stage for idea incubation in this game is also important. Moments of pause can help ensure the ideas that are put forward are the most suitable.

The Creativity Dice #creativity #problem solving #thiagi #issue analysis Too much linear thinking is hazardous to creative problem solving. To be creative, you should approach the problem (or the opportunity) from different points of view. You should leave a thought hanging in mid-air and move to another. This skipping around prevents premature closure and lets your brain incubate one line of thought while you consciously pursue another.

11. Fishbone Analysis

Organizational or team challenges are rarely simple, and it’s important to remember that one problem can be an indication of something that goes deeper and may require further consideration to be solved.

Fishbone Analysis helps groups to dig deeper and understand the origins of a problem. It’s a great example of a root cause analysis method that is simple for everyone on a team to get their head around.

Participants in this activity are asked to annotate a diagram of a fish, first adding the problem or issue to be worked on at the head of a fish before then brainstorming the root causes of the problem and adding them as bones on the fish.

Using abstractions such as a diagram of a fish can really help a team break out of their regular thinking and develop a creative approach.

Fishbone Analysis #problem solving ##root cause analysis #decision making #online facilitation A process to help identify and understand the origins of problems, issues or observations.

12. Problem Tree

Encouraging visual thinking can be an essential part of many strategies. By simply reframing and clarifying problems, a group can move towards developing a problem solving model that works for them.

In Problem Tree, groups are asked to first brainstorm a list of problems – these can be design problems, team problems or larger business problems – and then organize them into a hierarchy. The hierarchy could be from most important to least important or abstract to practical, though the key thing with problem solving games that involve this aspect is that your group has some way of managing and sorting all the issues that are raised.

Once you have a list of problems that need to be solved and have organized them accordingly, you’re then well-positioned for the next problem solving steps.

Problem tree #define intentions #create #design #issue analysis A problem tree is a tool to clarify the hierarchy of problems addressed by the team within a design project; it represents high level problems or related sublevel problems.

13. SWOT Analysis

Chances are you’ve heard of the SWOT Analysis before. This problem-solving method focuses on identifying strengths, weaknesses, opportunities, and threats is a tried and tested method for both individuals and teams.

Start by creating a desired end state or outcome and bare this in mind – any process solving model is made more effective by knowing what you are moving towards. Create a quadrant made up of the four categories of a SWOT analysis and ask participants to generate ideas based on each of those quadrants.

Once you have those ideas assembled in their quadrants, cluster them together based on their affinity with other ideas. These clusters are then used to facilitate group conversations and move things forward.

SWOT analysis #gamestorming #problem solving #action #meeting facilitation The SWOT Analysis is a long-standing technique of looking at what we have, with respect to the desired end state, as well as what we could improve on. It gives us an opportunity to gauge approaching opportunities and dangers, and assess the seriousness of the conditions that affect our future. When we understand those conditions, we can influence what comes next.

14. Agreement-Certainty Matrix

Not every problem-solving approach is right for every challenge, and deciding on the right method for the challenge at hand is a key part of being an effective team.

The Agreement Certainty matrix helps teams align on the nature of the challenges facing them. By sorting problems from simple to chaotic, your team can understand what methods are suitable for each problem and what they can do to ensure effective results.

If you are already using Liberating Structures techniques as part of your problem-solving strategy, the Agreement-Certainty Matrix can be an invaluable addition to your process. We’ve found it particularly if you are having issues with recurring problems in your organization and want to go deeper in understanding the root cause.

Agreement-Certainty Matrix #issue analysis #liberating structures #problem solving You can help individuals or groups avoid the frequent mistake of trying to solve a problem with methods that are not adapted to the nature of their challenge. The combination of two questions makes it possible to easily sort challenges into four categories: simple, complicated, complex , and chaotic . A problem is simple when it can be solved reliably with practices that are easy to duplicate. It is complicated when experts are required to devise a sophisticated solution that will yield the desired results predictably. A problem is complex when there are several valid ways to proceed but outcomes are not predictable in detail. Chaotic is when the context is too turbulent to identify a path forward. A loose analogy may be used to describe these differences: simple is like following a recipe, complicated like sending a rocket to the moon, complex like raising a child, and chaotic is like the game “Pin the Tail on the Donkey.” The Liberating Structures Matching Matrix in Chapter 5 can be used as the first step to clarify the nature of a challenge and avoid the mismatches between problems and solutions that are frequently at the root of chronic, recurring problems.

Organizing and charting a team’s progress can be important in ensuring its success. SQUID (Sequential Question and Insight Diagram) is a great model that allows a team to effectively switch between giving questions and answers and develop the skills they need to stay on track throughout the process.

Begin with two different colored sticky notes – one for questions and one for answers – and with your central topic (the head of the squid) on the board. Ask the group to first come up with a series of questions connected to their best guess of how to approach the topic. Ask the group to come up with answers to those questions, fix them to the board and connect them with a line. After some discussion, go back to question mode by responding to the generated answers or other points on the board.

It’s rewarding to see a diagram grow throughout the exercise, and a completed SQUID can provide a visual resource for future effort and as an example for other teams.

SQUID #gamestorming #project planning #issue analysis #problem solving When exploring an information space, it’s important for a group to know where they are at any given time. By using SQUID, a group charts out the territory as they go and can navigate accordingly. SQUID stands for Sequential Question and Insight Diagram.

16. Speed Boat

To continue with our nautical theme, Speed Boat is a short and sweet activity that can help a team quickly identify what employees, clients or service users might have a problem with and analyze what might be standing in the way of achieving a solution.

Methods that allow for a group to make observations, have insights and obtain those eureka moments quickly are invaluable when trying to solve complex problems.

In Speed Boat, the approach is to first consider what anchors and challenges might be holding an organization (or boat) back. Bonus points if you are able to identify any sharks in the water and develop ideas that can also deal with competitors!

Speed Boat #gamestorming #problem solving #action Speedboat is a short and sweet way to identify what your employees or clients don’t like about your product/service or what’s standing in the way of a desired goal.

17. The Journalistic Six

Some of the most effective ways of solving problems is by encouraging teams to be more inclusive and diverse in their thinking.

Based on the six key questions journalism students are taught to answer in articles and news stories, The Journalistic Six helps create teams to see the whole picture. By using who, what, when, where, why, and how to facilitate the conversation and encourage creative thinking, your team can make sure that the problem identification and problem analysis stages of the are covered exhaustively and thoughtfully. Reporter’s notebook and dictaphone optional.

The Journalistic Six – Who What When Where Why How #idea generation #issue analysis #problem solving #online #creative thinking #remote-friendly A questioning method for generating, explaining, investigating ideas.

18. LEGO Challenge

Now for an activity that is a little out of the (toy) box. LEGO Serious Play is a facilitation methodology that can be used to improve creative thinking and problem-solving skills.

The LEGO Challenge includes giving each member of the team an assignment that is hidden from the rest of the group while they create a structure without speaking.

What the LEGO challenge brings to the table is a fun working example of working with stakeholders who might not be on the same page to solve problems. Also, it’s LEGO! Who doesn’t love LEGO!

LEGO Challenge #hyperisland #team A team-building activity in which groups must work together to build a structure out of LEGO, but each individual has a secret “assignment” which makes the collaborative process more challenging. It emphasizes group communication, leadership dynamics, conflict, cooperation, patience and problem solving strategy.

19. What, So What, Now What?

If not carefully managed, the problem identification and problem analysis stages of the problem-solving process can actually create more problems and misunderstandings.

The What, So What, Now What? problem-solving activity is designed to help collect insights and move forward while also eliminating the possibility of disagreement when it comes to identifying, clarifying, and analyzing organizational or work problems.

Facilitation is all about bringing groups together so that might work on a shared goal and the best problem-solving strategies ensure that teams are aligned in purpose, if not initially in opinion or insight.

Throughout the three steps of this game, you give everyone on a team to reflect on a problem by asking what happened, why it is important, and what actions should then be taken.

This can be a great activity for bringing our individual perceptions about a problem or challenge and contextualizing it in a larger group setting. This is one of the most important problem-solving skills you can bring to your organization.

W³ – What, So What, Now What? #issue analysis #innovation #liberating structures You can help groups reflect on a shared experience in a way that builds understanding and spurs coordinated action while avoiding unproductive conflict. It is possible for every voice to be heard while simultaneously sifting for insights and shaping new direction. Progressing in stages makes this practical—from collecting facts about What Happened to making sense of these facts with So What and finally to what actions logically follow with Now What . The shared progression eliminates most of the misunderstandings that otherwise fuel disagreements about what to do. Voila!

20. Journalists

Problem analysis can be one of the most important and decisive stages of all problem-solving tools. Sometimes, a team can become bogged down in the details and are unable to move forward.

Journalists is an activity that can avoid a group from getting stuck in the problem identification or problem analysis stages of the process.

In Journalists, the group is invited to draft the front page of a fictional newspaper and figure out what stories deserve to be on the cover and what headlines those stories will have. By reframing how your problems and challenges are approached, you can help a team move productively through the process and be better prepared for the steps to follow.

Journalists #vision #big picture #issue analysis #remote-friendly This is an exercise to use when the group gets stuck in details and struggles to see the big picture. Also good for defining a vision.

Problem-solving techniques for developing solutions

The success of any problem-solving process can be measured by the solutions it produces. After you’ve defined the issue, explored existing ideas, and ideated, it’s time to narrow down to the correct solution.

Use these problem-solving techniques when you want to help your team find consensus, compare possible solutions, and move towards taking action on a particular problem.

Improved Solutions
Four-Step Sketch
15% Solutions
How-Now-Wow matrix
Impact Effort Matrix

21. Mindspin

Brainstorming is part of the bread and butter of the problem-solving process and all problem-solving strategies benefit from getting ideas out and challenging a team to generate solutions quickly.

With Mindspin, participants are encouraged not only to generate ideas but to do so under time constraints and by slamming down cards and passing them on. By doing multiple rounds, your team can begin with a free generation of possible solutions before moving on to developing those solutions and encouraging further ideation.

This is one of our favorite problem-solving activities and can be great for keeping the energy up throughout the workshop. Remember the importance of helping people become engaged in the process – energizing problem-solving techniques like Mindspin can help ensure your team stays engaged and happy, even when the problems they’re coming together to solve are complex.

MindSpin #teampedia #idea generation #problem solving #action A fast and loud method to enhance brainstorming within a team. Since this activity has more than round ideas that are repetitive can be ruled out leaving more creative and innovative answers to the challenge.

22. Improved Solutions

After a team has successfully identified a problem and come up with a few solutions, it can be tempting to call the work of the problem-solving process complete. That said, the first solution is not necessarily the best, and by including a further review and reflection activity into your problem-solving model, you can ensure your group reaches the best possible result.

One of a number of problem-solving games from Thiagi Group, Improved Solutions helps you go the extra mile and develop suggested solutions with close consideration and peer review. By supporting the discussion of several problems at once and by shifting team roles throughout, this problem-solving technique is a dynamic way of finding the best solution.

Improved Solutions #creativity #thiagi #problem solving #action #team You can improve any solution by objectively reviewing its strengths and weaknesses and making suitable adjustments. In this creativity framegame, you improve the solutions to several problems. To maintain objective detachment, you deal with a different problem during each of six rounds and assume different roles (problem owner, consultant, basher, booster, enhancer, and evaluator) during each round. At the conclusion of the activity, each player ends up with two solutions to her problem.

23. Four Step Sketch

Creative thinking and visual ideation does not need to be confined to the opening stages of your problem-solving strategies. Exercises that include sketching and prototyping on paper can be effective at the solution finding and development stage of the process, and can be great for keeping a team engaged.

By going from simple notes to a crazy 8s round that involves rapidly sketching 8 variations on their ideas before then producing a final solution sketch, the group is able to iterate quickly and visually. Problem-solving techniques like Four-Step Sketch are great if you have a group of different thinkers and want to change things up from a more textual or discussion-based approach.

Four-Step Sketch #design sprint #innovation #idea generation #remote-friendly The four-step sketch is an exercise that helps people to create well-formed concepts through a structured process that includes: Review key information Start design work on paper, Consider multiple variations , Create a detailed solution . This exercise is preceded by a set of other activities allowing the group to clarify the challenge they want to solve. See how the Four Step Sketch exercise fits into a Design Sprint

24. 15% Solutions

Some problems are simpler than others and with the right problem-solving activities, you can empower people to take immediate actions that can help create organizational change.

Part of the liberating structures toolkit, 15% solutions is a problem-solving technique that focuses on finding and implementing solutions quickly. A process of iterating and making small changes quickly can help generate momentum and an appetite for solving complex problems.

Problem-solving strategies can live and die on whether people are onboard. Getting some quick wins is a great way of getting people behind the process.

It can be extremely empowering for a team to realize that problem-solving techniques can be deployed quickly and easily and delineate between things they can positively impact and those things they cannot change.

15% Solutions #action #liberating structures #remote-friendly You can reveal the actions, however small, that everyone can do immediately. At a minimum, these will create momentum, and that may make a BIG difference. 15% Solutions show that there is no reason to wait around, feel powerless, or fearful. They help people pick it up a level. They get individuals and the group to focus on what is within their discretion instead of what they cannot change. With a very simple question, you can flip the conversation to what can be done and find solutions to big problems that are often distributed widely in places not known in advance. Shifting a few grains of sand may trigger a landslide and change the whole landscape.

25. How-Now-Wow Matrix

The problem-solving process is often creative, as complex problems usually require a change of thinking and creative response in order to find the best solutions. While it’s common for the first stages to encourage creative thinking, groups can often gravitate to familiar solutions when it comes to the end of the process.

When selecting solutions, you don’t want to lose your creative energy! The How-Now-Wow Matrix from Gamestorming is a great problem-solving activity that enables a group to stay creative and think out of the box when it comes to selecting the right solution for a given problem.

Problem-solving techniques that encourage creative thinking and the ideation and selection of new solutions can be the most effective in organisational change. Give the How-Now-Wow Matrix a go, and not just for how pleasant it is to say out loud.

How-Now-Wow Matrix #gamestorming #idea generation #remote-friendly When people want to develop new ideas, they most often think out of the box in the brainstorming or divergent phase. However, when it comes to convergence, people often end up picking ideas that are most familiar to them. This is called a ‘creative paradox’ or a ‘creadox’. The How-Now-Wow matrix is an idea selection tool that breaks the creadox by forcing people to weigh each idea on 2 parameters.

26. Impact and Effort Matrix

All problem-solving techniques hope to not only find solutions to a given problem or challenge but to find the best solution. When it comes to finding a solution, groups are invited to put on their decision-making hats and really think about how a proposed idea would work in practice.

The Impact and Effort Matrix is one of the problem-solving techniques that fall into this camp, empowering participants to first generate ideas and then categorize them into a 2×2 matrix based on impact and effort.

Activities that invite critical thinking while remaining simple are invaluable. Use the Impact and Effort Matrix to move from ideation and towards evaluating potential solutions before then committing to them.

Impact and Effort Matrix #gamestorming #decision making #action #remote-friendly In this decision-making exercise, possible actions are mapped based on two factors: effort required to implement and potential impact. Categorizing ideas along these lines is a useful technique in decision making, as it obliges contributors to balance and evaluate suggested actions before committing to them.

27. Dotmocracy

If you’ve followed each of the problem-solving steps with your group successfully, you should move towards the end of your process with heaps of possible solutions developed with a specific problem in mind. But how do you help a group go from ideation to putting a solution into action?

Dotmocracy – or Dot Voting -is a tried and tested method of helping a team in the problem-solving process make decisions and put actions in place with a degree of oversight and consensus.

One of the problem-solving techniques that should be in every facilitator’s toolbox, Dot Voting is fast and effective and can help identify the most popular and best solutions and help bring a group to a decision effectively.

Dotmocracy #action #decision making #group prioritization #hyperisland #remote-friendly Dotmocracy is a simple method for group prioritization or decision-making. It is not an activity on its own, but a method to use in processes where prioritization or decision-making is the aim. The method supports a group to quickly see which options are most popular or relevant. The options or ideas are written on post-its and stuck up on a wall for the whole group to see. Each person votes for the options they think are the strongest, and that information is used to inform a decision.

All facilitators know that warm-ups and icebreakers are useful for any workshop or group process. Problem-solving workshops are no different.

Use these problem-solving techniques to warm up a group and prepare them for the rest of the process. Activating your group by tapping into some of the top problem-solving skills can be one of the best ways to see great outcomes from your session.

Check-in/Check-out
Doodling Together
Show and Tell
Constellations
Draw a Tree

28. Check-in / Check-out

Solid processes are planned from beginning to end, and the best facilitators know that setting the tone and establishing a safe, open environment can be integral to a successful problem-solving process.

Check-in / Check-out is a great way to begin and/or bookend a problem-solving workshop. Checking in to a session emphasizes that everyone will be seen, heard, and expected to contribute.

If you are running a series of meetings, setting a consistent pattern of checking in and checking out can really help your team get into a groove. We recommend this opening-closing activity for small to medium-sized groups though it can work with large groups if they’re disciplined!

Check-in / Check-out #team #opening #closing #hyperisland #remote-friendly Either checking-in or checking-out is a simple way for a team to open or close a process, symbolically and in a collaborative way. Checking-in/out invites each member in a group to be present, seen and heard, and to express a reflection or a feeling. Checking-in emphasizes presence, focus and group commitment; checking-out emphasizes reflection and symbolic closure.

29. Doodling Together

Thinking creatively and not being afraid to make suggestions are important problem-solving skills for any group or team, and warming up by encouraging these behaviors is a great way to start.

Doodling Together is one of our favorite creative ice breaker games – it’s quick, effective, and fun and can make all following problem-solving steps easier by encouraging a group to collaborate visually. By passing cards and adding additional items as they go, the workshop group gets into a groove of co-creation and idea development that is crucial to finding solutions to problems.

Doodling Together #collaboration #creativity #teamwork #fun #team #visual methods #energiser #icebreaker #remote-friendly Create wild, weird and often funny postcards together & establish a group’s creative confidence.

30. Show and Tell

You might remember some version of Show and Tell from being a kid in school and it’s a great problem-solving activity to kick off a session.

Asking participants to prepare a little something before a workshop by bringing an object for show and tell can help them warm up before the session has even begun! Games that include a physical object can also help encourage early engagement before moving onto more big-picture thinking.

By asking your participants to tell stories about why they chose to bring a particular item to the group, you can help teams see things from new perspectives and see both differences and similarities in the way they approach a topic. Great groundwork for approaching a problem-solving process as a team!

Show and Tell #gamestorming #action #opening #meeting facilitation Show and Tell taps into the power of metaphors to reveal players’ underlying assumptions and associations around a topic The aim of the game is to get a deeper understanding of stakeholders’ perspectives on anything—a new project, an organizational restructuring, a shift in the company’s vision or team dynamic.

31. Constellations

Who doesn’t love stars? Constellations is a great warm-up activity for any workshop as it gets people up off their feet, energized, and ready to engage in new ways with established topics. It’s also great for showing existing beliefs, biases, and patterns that can come into play as part of your session.

Using warm-up games that help build trust and connection while also allowing for non-verbal responses can be great for easing people into the problem-solving process and encouraging engagement from everyone in the group. Constellations is great in large spaces that allow for movement and is definitely a practical exercise to allow the group to see patterns that are otherwise invisible.

Constellations #trust #connection #opening #coaching #patterns #system Individuals express their response to a statement or idea by standing closer or further from a central object. Used with teams to reveal system, hidden patterns, perspectives.

32. Draw a Tree

Problem-solving games that help raise group awareness through a central, unifying metaphor can be effective ways to warm-up a group in any problem-solving model.

Draw a Tree is a simple warm-up activity you can use in any group and which can provide a quick jolt of energy. Start by asking your participants to draw a tree in just 45 seconds – they can choose whether it will be abstract or realistic.

Once the timer is up, ask the group how many people included the roots of the tree and use this as a means to discuss how we can ignore important parts of any system simply because they are not visible.

All problem-solving strategies are made more effective by thinking of problems critically and by exposing things that may not normally come to light. Warm-up games like Draw a Tree are great in that they quickly demonstrate some key problem-solving skills in an accessible and effective way.

Draw a Tree #thiagi #opening #perspectives #remote-friendly With this game you can raise awarness about being more mindful, and aware of the environment we live in.

Each step of the problem-solving workshop benefits from an intelligent deployment of activities, games, and techniques. Bringing your session to an effective close helps ensure that solutions are followed through on and that you also celebrate what has been achieved.

Here are some problem-solving activities you can use to effectively close a workshop or meeting and ensure the great work you’ve done can continue afterward.

One Breath Feedback
Who What When Matrix
Response Cards

How do I conclude a problem-solving process?

All good things must come to an end. With the bulk of the work done, it can be tempting to conclude your workshop swiftly and without a moment to debrief and align. This can be problematic in that it doesn’t allow your team to fully process the results or reflect on the process.

At the end of an effective session, your team will have gone through a process that, while productive, can be exhausting. It’s important to give your group a moment to take a breath, ensure that they are clear on future actions, and provide short feedback before leaving the space.

The primary purpose of any problem-solving method is to generate solutions and then implement them. Be sure to take the opportunity to ensure everyone is aligned and ready to effectively implement the solutions you produced in the workshop.

Remember that every process can be improved and by giving a short moment to collect feedback in the session, you can further refine your problem-solving methods and see further success in the future too.

33. One Breath Feedback

Maintaining attention and focus during the closing stages of a problem-solving workshop can be tricky and so being concise when giving feedback can be important. It’s easy to incur “death by feedback” should some team members go on for too long sharing their perspectives in a quick feedback round.

One Breath Feedback is a great closing activity for workshops. You give everyone an opportunity to provide feedback on what they’ve done but only in the space of a single breath. This keeps feedback short and to the point and means that everyone is encouraged to provide the most important piece of feedback to them.

One breath feedback #closing #feedback #action This is a feedback round in just one breath that excels in maintaining attention: each participants is able to speak during just one breath … for most people that’s around 20 to 25 seconds … unless of course you’ve been a deep sea diver in which case you’ll be able to do it for longer.

34. Who What When Matrix

Matrices feature as part of many effective problem-solving strategies and with good reason. They are easily recognizable, simple to use, and generate results.

The Who What When Matrix is a great tool to use when closing your problem-solving session by attributing a who, what and when to the actions and solutions you have decided upon. The resulting matrix is a simple, easy-to-follow way of ensuring your team can move forward.

Great solutions can’t be enacted without action and ownership. Your problem-solving process should include a stage for allocating tasks to individuals or teams and creating a realistic timeframe for those solutions to be implemented or checked out. Use this method to keep the solution implementation process clear and simple for all involved.

Who/What/When Matrix #gamestorming #action #project planning With Who/What/When matrix, you can connect people with clear actions they have defined and have committed to.

35. Response cards

Group discussion can comprise the bulk of most problem-solving activities and by the end of the process, you might find that your team is talked out!

Providing a means for your team to give feedback with short written notes can ensure everyone is head and can contribute without the need to stand up and talk. Depending on the needs of the group, giving an alternative can help ensure everyone can contribute to your problem-solving model in the way that makes the most sense for them.

Response Cards is a great way to close a workshop if you are looking for a gentle warm-down and want to get some swift discussion around some of the feedback that is raised.

Response Cards #debriefing #closing #structured sharing #questions and answers #thiagi #action It can be hard to involve everyone during a closing of a session. Some might stay in the background or get unheard because of louder participants. However, with the use of Response Cards, everyone will be involved in providing feedback or clarify questions at the end of a session.

Save time and effort discovering the right solutions

A structured problem solving process is a surefire way of solving tough problems, discovering creative solutions and driving organizational change. But how can you design for successful outcomes?

With SessionLab, it’s easy to design engaging workshops that deliver results. Drag, drop and reorder blocks to build your agenda. When you make changes or update your agenda, your session timing adjusts automatically , saving you time on manual adjustments.

Collaborating with stakeholders or clients? Share your agenda with a single click and collaborate in real-time. No more sending documents back and forth over email.

Explore how to use SessionLab to design effective problem solving workshops or watch this five minute video to see the planner in action!

Over to you

The problem-solving process can often be as complicated and multifaceted as the problems they are set-up to solve. With the right problem-solving techniques and a mix of creative exercises designed to guide discussion and generate purposeful ideas, we hope we’ve given you the tools to find the best solutions as simply and easily as possible.

Is there a problem-solving technique that you are missing here? Do you have a favorite activity or method you use when facilitating? Let us know in the comments below, we’d love to hear from you!

thank you very much for these excellent techniques

Certainly wonderful article, very detailed. Shared!

Your list of techniques for problem solving can be helpfully extended by adding TRIZ to the list of techniques. TRIZ has 40 problem solving techniques derived from methods inventros and patent holders used to get new patents. About 10-12 are general approaches. many organization sponsor classes in TRIZ that are used to solve business problems or general organiztational problems. You can take a look at TRIZ and dwonload a free internet booklet to see if you feel it shound be included per your selection process.

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What is Problem Solving? (Steps, Techniques, Examples)

By Status.net Editorial Team on May 7, 2023 — 5 minutes to read

What Is Problem Solving?

Definition and importance.

Problem solving is the process of finding solutions to obstacles or challenges you encounter in your life or work. It is a crucial skill that allows you to tackle complex situations, adapt to changes, and overcome difficulties with ease. Mastering this ability will contribute to both your personal and professional growth, leading to more successful outcomes and better decision-making.

Problem-Solving Steps

The problem-solving process typically includes the following steps:

Identify the issue : Recognize the problem that needs to be solved.
Analyze the situation : Examine the issue in depth, gather all relevant information, and consider any limitations or constraints that may be present.
Generate potential solutions : Brainstorm a list of possible solutions to the issue, without immediately judging or evaluating them.
Evaluate options : Weigh the pros and cons of each potential solution, considering factors such as feasibility, effectiveness, and potential risks.
Select the best solution : Choose the option that best addresses the problem and aligns with your objectives.
Implement the solution : Put the selected solution into action and monitor the results to ensure it resolves the issue.
Review and learn : Reflect on the problem-solving process, identify any improvements or adjustments that can be made, and apply these learnings to future situations.

Defining the Problem

To start tackling a problem, first, identify and understand it. Analyzing the issue thoroughly helps to clarify its scope and nature. Ask questions to gather information and consider the problem from various angles. Some strategies to define the problem include:

Brainstorming with others
Asking the 5 Ws and 1 H (Who, What, When, Where, Why, and How)
Analyzing cause and effect
Creating a problem statement

Generating Solutions

Once the problem is clearly understood, brainstorm possible solutions. Think creatively and keep an open mind, as well as considering lessons from past experiences. Consider:

Creating a list of potential ideas to solve the problem
Grouping and categorizing similar solutions
Prioritizing potential solutions based on feasibility, cost, and resources required
Involving others to share diverse opinions and inputs

Evaluating and Selecting Solutions

Evaluate each potential solution, weighing its pros and cons. To facilitate decision-making, use techniques such as:

SWOT analysis (Strengths, Weaknesses, Opportunities, Threats)
Decision-making matrices
Pros and cons lists
Risk assessments

After evaluating, choose the most suitable solution based on effectiveness, cost, and time constraints.

Implementing and Monitoring the Solution

Implement the chosen solution and monitor its progress. Key actions include:

Communicating the solution to relevant parties
Setting timelines and milestones
Assigning tasks and responsibilities
Monitoring the solution and making adjustments as necessary
Evaluating the effectiveness of the solution after implementation

Utilize feedback from stakeholders and consider potential improvements. Remember that problem-solving is an ongoing process that can always be refined and enhanced.

Problem-Solving Techniques

During each step, you may find it helpful to utilize various problem-solving techniques, such as:

Brainstorming : A free-flowing, open-minded session where ideas are generated and listed without judgment, to encourage creativity and innovative thinking.
Root cause analysis : A method that explores the underlying causes of a problem to find the most effective solution rather than addressing superficial symptoms.
SWOT analysis : A tool used to evaluate the strengths, weaknesses, opportunities, and threats related to a problem or decision, providing a comprehensive view of the situation.
Mind mapping : A visual technique that uses diagrams to organize and connect ideas, helping to identify patterns, relationships, and possible solutions.

Brainstorming

When facing a problem, start by conducting a brainstorming session. Gather your team and encourage an open discussion where everyone contributes ideas, no matter how outlandish they may seem. This helps you:

Generate a diverse range of solutions
Encourage all team members to participate
Foster creative thinking

When brainstorming, remember to:

Reserve judgment until the session is over
Encourage wild ideas
Combine and improve upon ideas

Root Cause Analysis

For effective problem-solving, identifying the root cause of the issue at hand is crucial. Try these methods:

5 Whys : Ask “why” five times to get to the underlying cause.
Fishbone Diagram : Create a diagram representing the problem and break it down into categories of potential causes.
Pareto Analysis : Determine the few most significant causes underlying the majority of problems.

SWOT Analysis

SWOT analysis helps you examine the Strengths, Weaknesses, Opportunities, and Threats related to your problem. To perform a SWOT analysis:

List your problem’s strengths, such as relevant resources or strong partnerships.
Identify its weaknesses, such as knowledge gaps or limited resources.
Explore opportunities, like trends or new technologies, that could help solve the problem.
Recognize potential threats, like competition or regulatory barriers.

SWOT analysis aids in understanding the internal and external factors affecting the problem, which can help guide your solution.

Mind Mapping

A mind map is a visual representation of your problem and potential solutions. It enables you to organize information in a structured and intuitive manner. To create a mind map:

Write the problem in the center of a blank page.
Draw branches from the central problem to related sub-problems or contributing factors.
Add more branches to represent potential solutions or further ideas.

Mind mapping allows you to visually see connections between ideas and promotes creativity in problem-solving.

Examples of Problem Solving in Various Contexts

In the business world, you might encounter problems related to finances, operations, or communication. Applying problem-solving skills in these situations could look like:

Identifying areas of improvement in your company’s financial performance and implementing cost-saving measures
Resolving internal conflicts among team members by listening and understanding different perspectives, then proposing and negotiating solutions
Streamlining a process for better productivity by removing redundancies, automating tasks, or re-allocating resources

In educational contexts, problem-solving can be seen in various aspects, such as:

Addressing a gap in students’ understanding by employing diverse teaching methods to cater to different learning styles
Developing a strategy for successful time management to balance academic responsibilities and extracurricular activities
Seeking resources and support to provide equal opportunities for learners with special needs or disabilities

Everyday life is full of challenges that require problem-solving skills. Some examples include:

Overcoming a personal obstacle, such as improving your fitness level, by establishing achievable goals, measuring progress, and adjusting your approach accordingly
Navigating a new environment or city by researching your surroundings, asking for directions, or using technology like GPS to guide you
Dealing with a sudden change, like a change in your work schedule, by assessing the situation, identifying potential impacts, and adapting your plans to accommodate the change.
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10 Problem-solving strategies to turn challenges on their head

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What is an example of problem-solving?

What are the 5 steps to problem-solving, 10 effective problem-solving strategies, what skills do efficient problem solvers have, how to improve your problem-solving skills.

Problems come in all shapes and sizes — from workplace conflict to budget cuts.

Creative problem-solving is one of the most in-demand skills in all roles and industries. It can boost an organization’s human capital and give it a competitive edge.

Problem-solving strategies are ways of approaching problems that can help you look beyond the obvious answers and find the best solution to your problem .

Let’s take a look at a five-step problem-solving process and how to combine it with proven problem-solving strategies. This will give you the tools and skills to solve even your most complex problems.

Good problem-solving is an essential part of the decision-making process . To see what a problem-solving process might look like in real life, let’s take a common problem for SaaS brands — decreasing customer churn rates.

To solve this problem, the company must first identify it. In this case, the problem is that the churn rate is too high.

Next, they need to identify the root causes of the problem. This could be anything from their customer service experience to their email marketing campaigns. If there are several problems, they will need a separate problem-solving process for each one.

Let’s say the problem is with email marketing — they’re not nurturing existing customers. Now that they’ve identified the problem, they can start using problem-solving strategies to look for solutions.

This might look like coming up with special offers, discounts, or bonuses for existing customers. They need to find ways to remind them to use their products and services while providing added value. This will encourage customers to keep paying their monthly subscriptions.

They might also want to add incentives, such as access to a premium service at no extra cost after 12 months of membership. They could publish blog posts that help their customers solve common problems and share them as an email newsletter.

The company should set targets and a time frame in which to achieve them. This will allow leaders to measure progress and identify which actions yield the best results.

Perhaps you’ve got a problem you need to tackle. Or maybe you want to be prepared the next time one arises. Either way, it’s a good idea to get familiar with the five steps of problem-solving.

Use this step-by-step problem-solving method with the strategies in the following section to find possible solutions to your problem.

1. Identify the problem

The first step is to know which problem you need to solve. Then, you need to find the root cause of the problem.

The best course of action is to gather as much data as possible, speak to the people involved, and separate facts from opinions.

Once this is done, formulate a statement that describes the problem. Use rational persuasion to make sure your team agrees .

2. Break the problem down

Identifying the problem allows you to see which steps need to be taken to solve it.

First, break the problem down into achievable blocks. Then, use strategic planning to set a time frame in which to solve the problem and establish a timeline for the completion of each stage.

3. Generate potential solutions

At this stage, the aim isn’t to evaluate possible solutions but to generate as many ideas as possible.

Encourage your team to use creative thinking and be patient — the best solution may not be the first or most obvious one.

Use one or more of the different strategies in the following section to help come up with solutions — the more creative, the better.

4. Evaluate the possible solutions

Once you’ve generated potential solutions, narrow them down to a shortlist. Then, evaluate the options on your shortlist.

There are usually many factors to consider. So when evaluating a solution, ask yourself the following questions:

Will my team be on board with the proposition?
Does the solution align with organizational goals ?
Is the solution likely to achieve the desired outcomes?
Is the solution realistic and possible with current resources and constraints?
Will the solution solve the problem without causing additional unintended problems?

woman-helping-her-colleague-problem-solving-strategies

5. Implement and monitor the solutions

Once you’ve identified your solution and got buy-in from your team, it’s time to implement it.

But the work doesn’t stop there. You need to monitor your solution to see whether it actually solves your problem.

Request regular feedback from the team members involved and have a monitoring and evaluation plan in place to measure progress.

If the solution doesn’t achieve your desired results, start this step-by-step process again.

There are many different ways to approach problem-solving. Each is suitable for different types of problems.

The most appropriate problem-solving techniques will depend on your specific problem. You may need to experiment with several strategies before you find a workable solution.

Here are 10 effective problem-solving strategies for you to try:

Use a solution that worked before
Brainstorming
Work backward
Use the Kipling method
Draw the problem
Use trial and error
Sleep on it
Get advice from your peers
Use the Pareto principle
Add successful solutions to your toolkit

Let’s break each of these down.

1. Use a solution that worked before

It might seem obvious, but if you’ve faced similar problems in the past, look back to what worked then. See if any of the solutions could apply to your current situation and, if so, replicate them.

2. Brainstorming

The more people you enlist to help solve the problem, the more potential solutions you can come up with.

Use different brainstorming techniques to workshop potential solutions with your team. They’ll likely bring something you haven’t thought of to the table.

3. Work backward

Working backward is a way to reverse engineer your problem. Imagine your problem has been solved, and make that the starting point.

Then, retrace your steps back to where you are now. This can help you see which course of action may be most effective.

4. Use the Kipling method

This is a method that poses six questions based on Rudyard Kipling’s poem, “ I Keep Six Honest Serving Men .”

What is the problem?
Why is the problem important?
When did the problem arise, and when does it need to be solved?
How did the problem happen?
Where is the problem occurring?
Who does the problem affect?

Answering these questions can help you identify possible solutions.

5. Draw the problem

Sometimes it can be difficult to visualize all the components and moving parts of a problem and its solution. Drawing a diagram can help.

This technique is particularly helpful for solving process-related problems. For example, a product development team might want to decrease the time they take to fix bugs and create new iterations. Drawing the processes involved can help you see where improvements can be made.

woman-drawing-mind-map-problem-solving-strategies

6. Use trial-and-error

A trial-and-error approach can be useful when you have several possible solutions and want to test them to see which one works best.

7. Sleep on it

Finding the best solution to a problem is a process. Remember to take breaks and get enough rest . Sometimes, a walk around the block can bring inspiration, but you should sleep on it if possible.

A good night’s sleep helps us find creative solutions to problems. This is because when you sleep, your brain sorts through the day’s events and stores them as memories. This enables you to process your ideas at a subconscious level.

If possible, give yourself a few days to develop and analyze possible solutions. You may find you have greater clarity after sleeping on it. Your mind will also be fresh, so you’ll be able to make better decisions.

8. Get advice from your peers

Getting input from a group of people can help you find solutions you may not have thought of on your own.

For solo entrepreneurs or freelancers, this might look like hiring a coach or mentor or joining a mastermind group.

For leaders , it might be consulting other members of the leadership team or working with a business coach .

It’s important to recognize you might not have all the skills, experience, or knowledge necessary to find a solution alone.

9. Use the Pareto principle

The Pareto principle — also known as the 80/20 rule — can help you identify possible root causes and potential solutions for your problems.

Although it’s not a mathematical law, it’s a principle found throughout many aspects of business and life. For example, 20% of the sales reps in a company might close 80% of the sales.

You may be able to narrow down the causes of your problem by applying the Pareto principle. This can also help you identify the most appropriate solutions.

10. Add successful solutions to your toolkit

Every situation is different, and the same solutions might not always work. But by keeping a record of successful problem-solving strategies, you can build up a solutions toolkit.

These solutions may be applicable to future problems. Even if not, they may save you some of the time and work needed to come up with a new solution.

three-colleagues-looking-at-computer-problem-solving-strategies

Improving problem-solving skills is essential for professional development — both yours and your team’s. Here are some of the key skills of effective problem solvers:

Critical thinking and analytical skills
Communication skills , including active listening
Decision-making
Planning and prioritization
Emotional intelligence , including empathy and emotional regulation
Time management
Data analysis
Research skills
Project management

And they see problems as opportunities. Everyone is born with problem-solving skills. But accessing these abilities depends on how we view problems. Effective problem-solvers see problems as opportunities to learn and improve.

Ready to work on your problem-solving abilities? Get started with these seven tips.

1. Build your problem-solving skills

One of the best ways to improve your problem-solving skills is to learn from experts. Consider enrolling in organizational training , shadowing a mentor , or working with a coach .

2. Practice

Practice using your new problem-solving skills by applying them to smaller problems you might encounter in your daily life.

Alternatively, imagine problematic scenarios that might arise at work and use problem-solving strategies to find hypothetical solutions.

3. Don’t try to find a solution right away

Often, the first solution you think of to solve a problem isn’t the most appropriate or effective.

Instead of thinking on the spot, give yourself time and use one or more of the problem-solving strategies above to activate your creative thinking.

two-colleagues-talking-at-corporate-event-problem-solving-strategies

4. Ask for feedback

Receiving feedback is always important for learning and growth. Your perception of your problem-solving skills may be different from that of your colleagues. They can provide insights that help you improve.

5. Learn new approaches and methodologies

There are entire books written about problem-solving methodologies if you want to take a deep dive into the subject.

We recommend starting with “ Fixed — How to Perfect the Fine Art of Problem Solving ” by Amy E. Herman.

6. Experiment

Tried-and-tested problem-solving techniques can be useful. However, they don’t teach you how to innovate and develop your own problem-solving approaches.

Sometimes, an unconventional approach can lead to the development of a brilliant new idea or strategy. So don’t be afraid to suggest your most “out there” ideas.

7. Analyze the success of your competitors

Do you have competitors who have already solved the problem you’re facing? Look at what they did, and work backward to solve your own problem.

For example, Netflix started in the 1990s as a DVD mail-rental company. Its main competitor at the time was Blockbuster.

But when streaming became the norm in the early 2000s, both companies faced a crisis. Netflix innovated, unveiling its streaming service in 2007.

If Blockbuster had followed Netflix’s example, it might have survived. Instead, it declared bankruptcy in 2010.

Use problem-solving strategies to uplevel your business

When facing a problem, it’s worth taking the time to find the right solution.

Otherwise, we risk either running away from our problems or headlong into solutions. When we do this, we might miss out on other, better options.

Use the problem-solving strategies outlined above to find innovative solutions to your business’ most perplexing problems.

If you’re ready to take problem-solving to the next level, request a demo with BetterUp . Our expert coaches specialize in helping teams develop and implement strategies that work.

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Elizabeth Perry, ACC

Elizabeth Perry is a Coach Community Manager at BetterUp. She uses strategic engagement strategies to cultivate a learning community across a global network of Coaches through in-person and virtual experiences, technology-enabled platforms, and strategic coaching industry partnerships. With over 3 years of coaching experience and a certification in transformative leadership and life coaching from Sofia University, Elizabeth leverages transpersonal psychology expertise to help coaches and clients gain awareness of their behavioral and thought patterns, discover their purpose and passions, and elevate their potential. She is a lifelong student of psychology, personal growth, and human potential as well as an ICF-certified ACC transpersonal life and leadership Coach.

8 creative solutions to your most challenging problems

5 problem-solving questions to prepare you for your next interview, what are metacognitive skills examples in everyday life, what is lateral thinking 7 techniques to encourage creative ideas, 31 examples of problem solving performance review phrases, learn what process mapping is and how to create one (+ examples), leadership activities that encourage employee engagement, can dreams help you solve problems 6 ways to try, how much do distractions cost 8 effects of lack of focus, similar articles, the pareto principle: how the 80/20 rule can help you do more with less, thinking outside the box: 8 ways to become a creative problem solver, 3 problem statement examples and steps to write your own, contingency planning: 4 steps to prepare for the unexpected, learn to sweat the small stuff: how to improve attention to detail, stay connected with betterup, get our newsletter, event invites, plus product insights and research..

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Overview of the Problem-Solving Mental Process

Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

Rachel Goldman, PhD FTOS, is a licensed psychologist, clinical assistant professor, speaker, wellness expert specializing in eating behaviors, stress management, and health behavior change.

Identify the Problem
Define the Problem
Form a Strategy
Organize Information
Allocate Resources
Monitor Progress
Evaluate the Results

Frequently Asked Questions

Problem-solving is a mental process that involves discovering, analyzing, and solving problems. The ultimate goal of problem-solving is to overcome obstacles and find a solution that best resolves the issue.

The best strategy for solving a problem depends largely on the unique situation. In some cases, people are better off learning everything they can about the issue and then using factual knowledge to come up with a solution. In other instances, creativity and insight are the best options.

It is not necessary to follow problem-solving steps sequentially, It is common to skip steps or even go back through steps multiple times until the desired solution is reached.

In order to correctly solve a problem, it is often important to follow a series of steps. Researchers sometimes refer to this as the problem-solving cycle. While this cycle is portrayed sequentially, people rarely follow a rigid series of steps to find a solution.

The following steps include developing strategies and organizing knowledge.

1. Identifying the Problem

While it may seem like an obvious step, identifying the problem is not always as simple as it sounds. In some cases, people might mistakenly identify the wrong source of a problem, which will make attempts to solve it inefficient or even useless.

Some strategies that you might use to figure out the source of a problem include :

Asking questions about the problem
Breaking the problem down into smaller pieces
Looking at the problem from different perspectives
Conducting research to figure out what relationships exist between different variables

2. Defining the Problem

After the problem has been identified, it is important to fully define the problem so that it can be solved. You can define a problem by operationally defining each aspect of the problem and setting goals for what aspects of the problem you will address

At this point, you should focus on figuring out which aspects of the problems are facts and which are opinions. State the problem clearly and identify the scope of the solution.

3. Forming a Strategy

After the problem has been identified, it is time to start brainstorming potential solutions. This step usually involves generating as many ideas as possible without judging their quality. Once several possibilities have been generated, they can be evaluated and narrowed down.

The next step is to develop a strategy to solve the problem. The approach used will vary depending upon the situation and the individual's unique preferences. Common problem-solving strategies include heuristics and algorithms.

Heuristics are mental shortcuts that are often based on solutions that have worked in the past. They can work well if the problem is similar to something you have encountered before and are often the best choice if you need a fast solution.
Algorithms are step-by-step strategies that are guaranteed to produce a correct result. While this approach is great for accuracy, it can also consume time and resources.

Heuristics are often best used when time is of the essence, while algorithms are a better choice when a decision needs to be as accurate as possible.

4. Organizing Information

Before coming up with a solution, you need to first organize the available information. What do you know about the problem? What do you not know? The more information that is available the better prepared you will be to come up with an accurate solution.

When approaching a problem, it is important to make sure that you have all the data you need. Making a decision without adequate information can lead to biased or inaccurate results.

5. Allocating Resources

Of course, we don't always have unlimited money, time, and other resources to solve a problem. Before you begin to solve a problem, you need to determine how high priority it is.

If it is an important problem, it is probably worth allocating more resources to solving it. If, however, it is a fairly unimportant problem, then you do not want to spend too much of your available resources on coming up with a solution.

At this stage, it is important to consider all of the factors that might affect the problem at hand. This includes looking at the available resources, deadlines that need to be met, and any possible risks involved in each solution. After careful evaluation, a decision can be made about which solution to pursue.

6. Monitoring Progress

After selecting a problem-solving strategy, it is time to put the plan into action and see if it works. This step might involve trying out different solutions to see which one is the most effective.

It is also important to monitor the situation after implementing a solution to ensure that the problem has been solved and that no new problems have arisen as a result of the proposed solution.

Effective problem-solvers tend to monitor their progress as they work towards a solution. If they are not making good progress toward reaching their goal, they will reevaluate their approach or look for new strategies .

7. Evaluating the Results

After a solution has been reached, it is important to evaluate the results to determine if it is the best possible solution to the problem. This evaluation might be immediate, such as checking the results of a math problem to ensure the answer is correct, or it can be delayed, such as evaluating the success of a therapy program after several months of treatment.

Once a problem has been solved, it is important to take some time to reflect on the process that was used and evaluate the results. This will help you to improve your problem-solving skills and become more efficient at solving future problems.

A Word From Verywell

It is important to remember that there are many different problem-solving processes with different steps, and this is just one example. Problem-solving in real-world situations requires a great deal of resourcefulness, flexibility, resilience, and continuous interaction with the environment.

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You can become a better problem solving by:

Practicing brainstorming and coming up with multiple potential solutions to problems
Being open-minded and considering all possible options before making a decision
Breaking down problems into smaller, more manageable pieces
Asking for help when needed
Researching different problem-solving techniques and trying out new ones
Learning from mistakes and using them as opportunities to grow

It's important to communicate openly and honestly with your partner about what's going on. Try to see things from their perspective as well as your own. Work together to find a resolution that works for both of you. Be willing to compromise and accept that there may not be a perfect solution.

Take breaks if things are getting too heated, and come back to the problem when you feel calm and collected. Don't try to fix every problem on your own—consider asking a therapist or counselor for help and insight.

If you've tried everything and there doesn't seem to be a way to fix the problem, you may have to learn to accept it. This can be difficult, but try to focus on the positive aspects of your life and remember that every situation is temporary. Don't dwell on what's going wrong—instead, think about what's going right. Find support by talking to friends or family. Seek professional help if you're having trouble coping.

Davidson JE, Sternberg RJ, editors. The Psychology of Problem Solving . Cambridge University Press; 2003. doi:10.1017/CBO9780511615771

Sarathy V. Real world problem-solving . Front Hum Neurosci . 2018;12:261. Published 2018 Jun 26. doi:10.3389/fnhum.2018.00261

By Kendra Cherry, MSEd Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

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A guide to problem-solving techniques, steps, and skills

You might associate problem-solving with the math exercises that a seven-year-old would do at school. But problem-solving isn’t just about math — it’s a crucial skill that helps everyone make better decisions in everyday life or work.

A guide to problem-solving techniques, steps, and skills

Problem-solving involves finding effective solutions to address complex challenges, in any context they may arise.

Unfortunately, structured and systematic problem-solving methods aren’t commonly taught. Instead, when solving a problem, PMs tend to rely heavily on intuition. While for simple issues this might work well, solving a complex problem with a straightforward solution is often ineffective and can even create more problems.

In this article, you’ll learn a framework for approaching problem-solving, alongside how you can improve your problem-solving skills.

The 7 steps to problem-solving

When it comes to problem-solving there are seven key steps that you should follow: define the problem, disaggregate, prioritize problem branches, create an analysis plan, conduct analysis, synthesis, and communication.

1. Define the problem

Problem-solving begins with a clear understanding of the issue at hand. Without a well-defined problem statement, confusion and misunderstandings can hinder progress. It’s crucial to ensure that the problem statement is outcome-focused, specific, measurable whenever possible, and time-bound.

Additionally, aligning the problem definition with relevant stakeholders and decision-makers is essential to ensure efforts are directed towards addressing the actual problem rather than side issues.

2. Disaggregate

Complex issues often require deeper analysis. Instead of tackling the entire problem at once, the next step is to break it down into smaller, more manageable components.

Various types of logic trees (also known as issue trees or decision trees) can be used to break down the problem. At each stage where new branches are created, it’s important for them to be “MECE” – mutually exclusive and collectively exhaustive. This process of breaking down continues until manageable components are identified, allowing for individual examination.

The decomposition of the problem demands looking at the problem from various perspectives. That is why collaboration within a team often yields more valuable results, as diverse viewpoints lead to a richer pool of ideas and solutions.

3. Prioritize problem branches

The next step involves prioritization. Not all branches of the problem tree have the same impact, so it’s important to understand the significance of each and focus attention on the most impactful areas. Prioritizing helps streamline efforts and minimize the time required to solve the problem.

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4. Create an analysis plan

For prioritized components, you may need to conduct in-depth analysis. Before proceeding, a work plan is created for data gathering and analysis. If work is conducted within a team, having a plan provides guidance on what needs to be achieved, who is responsible for which tasks, and the timelines involved.

5. Conduct analysis

Data gathering and analysis are central to the problem-solving process. It’s a good practice to set time limits for this phase to prevent excessive time spent on perfecting details. You can employ heuristics and rule-of-thumb reasoning to improve efficiency and direct efforts towards the most impactful work.

6. Synthesis

After each individual branch component has been researched, the problem isn’t solved yet. The next step is synthesizing the data logically to address the initial question. The synthesis process and the logical relationship between the individual branch results depend on the logic tree used.

7. Communication

The last step is communicating the story and the solution of the problem to the stakeholders and decision-makers. Clear effective communication is necessary to build trust in the solution and facilitates understanding among all parties involved. It ensures that stakeholders grasp the intricacies of the problem and the proposed solution, leading to informed decision-making.

Exploring problem-solving in various contexts

While problem-solving has traditionally been associated with fields like engineering and science, today it has become a fundamental skill for individuals across all professions. In fact, problem-solving consistently ranks as one of the top skills required by employers.

Problem-solving techniques can be applied in diverse contexts:

Individuals — What career path should I choose? Where should I live? These are examples of simple and common personal challenges that require effective problem-solving skills
Organizations — Businesses also face many decisions that are not trivial to answer. Should we expand into new markets this year? How can we enhance the quality of our product development? Will our office accommodate the upcoming year’s growth in terms of capacity?
Societal issues — The biggest world challenges are also complex problems that can be addressed with the same technique. How can we minimize the impact of climate change? How do we fight cancer?

Despite the variation in domains and contexts, the fundamental approach to solving these questions remains the same. It starts with gaining a clear understanding of the problem, followed by decomposition, conducting analysis of the decomposed branches, and synthesizing it into a result that answers the initial problem.

Real-world examples of problem-solving

Let’s now explore some examples where we can apply the problem solving framework.

Problem: In the production of electronic devices, you observe an increasing number of defects. How can you reduce the error rate and improve the quality?

Before delving into analysis, you can deprioritize branches that you already have information for or ones you deem less important. For instance, while transportation delays may occur, the resulting material degradation is likely negligible. For other branches, additional research and data gathering may be necessary.

Once results are obtained, synthesis is crucial to address the core question: How can you decrease the defect rate?

While all factors listed may play a role, their significance varies. Your task is to prioritize effectively. Through data analysis, you may discover that altering the equipment would bring the most substantial positive outcome. However, executing a solution isn’t always straightforward. In prioritizing, you should consider both the potential impact and the level of effort needed for implementation.

By evaluating impact and effort, you can systematically prioritize areas for improvement, focusing on those with high impact and requiring minimal effort to address. This approach ensures efficient allocation of resources towards improvements that offer the greatest return on investment.

Problem : What should be my next job role?

When breaking down this problem, you need to consider various factors that are important for your future happiness in the role. This includes aspects like the company culture, our interest in the work itself, and the lifestyle that you can afford with the role.

However, not all factors carry the same weight for us. To make sense of the results, we can assign a weight factor to each branch. For instance, passion for the job role may have a weight factor of 1, while interest in the industry may have a weight factor of 0.5, because that is less important for you.

By applying these weights to a specific role and summing the values, you can have an estimate of how suitable that role is for you. Moreover, you can compare two roles and make an informed decision based on these weighted indicators.

Key problem-solving skills

This framework provides the foundation and guidance needed to effectively solve problems. However, successfully applying this framework requires the following:

Creativity — During the decomposition phase, it’s essential to approach the problem from various perspectives and think outside the box to generate innovative ideas for breaking down the problem tree
Decision-making — Throughout the process, decisions must be made, even when full confidence is lacking. Employing rules of thumb to simplify analysis or selecting one tree cut over another requires decisiveness and comfort with choices made
Analytical skills — Analytical and research skills are necessary for the phase following decomposition, involving data gathering and analysis on selected tree branches
Teamwork — Collaboration and teamwork are crucial when working within a team setting. Solving problems effectively often requires collective effort and shared responsibility
Communication — Clear and structured communication is essential to convey the problem solution to stakeholders and decision-makers and build trust

How to enhance your problem-solving skills

Problem-solving requires practice and a certain mindset. The more you practice, the easier it becomes. Here are some strategies to enhance your skills:

Practice structured thinking in your daily life — Break down problems or questions into manageable parts. You don’t need to go through the entire problem-solving process and conduct detailed analysis. When conveying a message, simplify the conversation by breaking the message into smaller, more understandable segments
Regularly challenging yourself with games and puzzles — Solving puzzles, riddles, or strategy games can boost your problem-solving skills and cognitive agility.
Engage with individuals from diverse backgrounds and viewpoints — Conversing with people who offer different perspectives provides fresh insights and alternative solutions to problems. This boosts creativity and helps in approaching challenges from new angles

Final thoughts

Problem-solving extends far beyond mathematics or scientific fields; it’s a critical skill for making informed decisions in every area of life and work. The seven-step framework presented here provides a systematic approach to problem-solving, relevant across various domains.

Now, consider this: What’s one question currently on your mind? Grab a piece of paper and try to apply the problem-solving framework. You might uncover fresh insights you hadn’t considered before.

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What Is Problem Solving?

Find a solution to any problem you face..

By the Mind Tools Content Team

We all spend a lot of our time solving problems, both at work and in our personal lives.

Some problems are small, and we can quickly sort them out ourselves. But others are complex challenges that take collaboration, creativity, and a considerable amount of effort to solve.

At work, the types of problems we face depend largely on the organizations we're in and the jobs we do. A manager in a cleaning company, for example, might spend their day untangling staffing issues, resolving client complaints, and sorting out problems with equipment and supplies. An aircraft designer, on the other hand, might be grappling with a problem about aerodynamics, or trying to work out why a new safety feature isn't working. Meanwhile, a politician might be exploring solutions to racial injustice or climate change.

But whatever issues we face, there are some common ways to tackle them effectively. And we can all boost our confidence and ability to succeed by building a strong set of problem-solving skills.

Mind Tools offers a large collection of resources to help you do just that!

How Well Do You Solve Problems?

Start by taking an honest look at your existing skills. What's your current approach to solving problems, and how well is it working? Our quiz, How Good Is Your Problem Solving? lets you analyze your abilities, and signposts ways to address any areas of weakness.

Define Every Problem

The first step in solving a problem is understanding what that problem actually is. You need to be sure that you're dealing with the real problem – not its symptoms. For example, if performance in your department is substandard, you might think that the problem lies with the individuals submitting work. However, if you look a bit deeper, the real issue might be a general lack of training, or an unreasonable workload across the team.

Tools like 5 Whys , Appreciation and Root Cause Analysis get you asking the right questions, and help you to work through the layers of a problem to uncover what's really going on.

However, defining a problem doesn't mean deciding how to solve it straightaway. It's important to look at the issue from a variety of perspectives. If you commit yourself too early, you can end up with a short-sighted solution. The CATWOE checklist provides a powerful reminder to look at many elements that may contribute to the problem, keeping you open to a variety of possible solutions.

Understanding Complexity

As you define your problem, you'll often discover just how complicated it is. There are likely several interrelated issues involved. That's why it's important to have ways to visualize, simplify and make sense of this tangled mess!

Affinity Diagrams are great for organizing many different pieces of information into common themes, and for understanding the relationships between them.

Another popular tool is the Cause-and-Effect Diagram . To generate viable solutions, you need a solid understanding of what's causing the problem.

When your problem occurs within a business process, creating a Flow Chart , Swim Lane Diagram or a Systems Diagram will help you to see how various activities and inputs fit together. This may well highlight a missing element or bottleneck that's causing your problem.

Quite often, what seems to be a single problem turns out to be a whole series of problems. The Drill Down technique prompts you to split your problem into smaller, more manageable parts.

General Problem-Solving Tools

When you understand the problem in front of you, you’re ready to start solving it. With your definition to guide you, you can generate several possible solutions, choose the best one, then put it into action. That's the four-step approach at the heart of good problem solving.

There are various problem-solving styles to use. For example:

Constructive Controversy is a way of widening perspectives and energizing discussions.
Inductive Reasoning makes the most of people’s experiences and know-how, and can speed up solution finding.
Means-End Analysis can bring extra clarity to your thinking, and kick-start the process of implementing solutions.

Specific Problem-Solving Systems

Some particularly complicated or important problems call for a more comprehensive process. Again, Mind Tools has a range of approaches to try, including:

Simplex , which involves an eight-stage process: problem finding, fact finding, defining the problem, idea finding, selecting and evaluating, planning, selling the idea, and acting. These steps build upon the basic, four-step process described above, and they create a cycle of problem finding and solving that will continually improve your organization.
Appreciative Inquiry , which is a uniquely positive way of solving problems by examining what's working well in the areas surrounding them.
Soft Systems Methodology , which takes you through four stages to uncover more details about what's creating your problem, and then define actions that will improve the situation.

Further Problem-Solving Strategies

Good problem solving requires a number of other skills – all of which are covered by Mind Tools.

For example, we have a large section of resources to improve your Creativity , so that you come up with a range of possible solutions.

By strengthening your Decision Making , you'll be better at evaluating the options, selecting the best ones, then choosing how to implement them.

And our Project Management collection has valuable advice for strengthening the whole problem-solving process. The resources there will help you to make effective changes – and then keep them working long term.

Problems are an inescapable part of life, both in and out of work. So we can all benefit from having strong problem-solving skills.

It's important to understand your current approach to problem solving, and to know where and how to improve.

Define every problem you encounter – and understand its complexity, rather than trying to solve it too soon.

There's a range of general problem-solving approaches, helping you to generate possible answers, choose the best ones, and then implement your solution.

Some complicated or serious problems require more specific problem-solving systems, especially when they relate to business processes.

By boosting your creativity, decision-making and project-management skills, you’ll become even better at solving all the problems you face.

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Learn Creative Problem Solving Techniques to Stimulate Innovation in Your Organization

By Kate Eby | October 20, 2017 (updated August 27, 2021)

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In today’s competitive business landscape, organizations need processes in place to make strong, well-informed, and innovative decisions. Problem solving - in particular creative problem solving (CPS) - is a key skill in learning how to accurately identify problems and their causes, generate potential solutions, and evaluate all the possibilities to arrive at a strong corrective course of action. Every team in any organization, regardless of department or industry, needs to be effective, creative, and quick when solving problems.

In this article, we’ll discuss traditional and creative problem solving, and define the steps, best practices, and common barriers associated. After that, we’ll provide helpful methods and tools to identify the cause(s) of problematic situations, so you can get to the root of the issue and start to generate solutions. Then, we offer nearly 20 creative problem solving techniques to implement at your organization, or even in your personal life. Along the way, experts weigh in on the importance of problem solving, and offer tips and tricks.

What Is Problem Solving and Decision Making?

Problem solving is the process of working through every aspect of an issue or challenge to reach a solution. Decision making is choosing one of multiple proposed solutions — therefore, this process also includes defining and evaluating all potential options. Decision making is often one step of the problem solving process, but the two concepts are distinct.

Collective problem solving is problem solving that includes many different parties and bridges the knowledge of different groups. Collective problem solving is common in business problem solving because workplace decisions typically affect more than one person.

Problem solving, especially in business, is a complicated science. Not only are business conflicts multifaceted, but they often involve different personalities, levels of authority, and group dynamics. In recent years, however, there has been a rise in psychology-driven problem solving techniques, especially for the workplace. In fact, the psychology of how people solve problems is now studied formally in academic disciplines such as psychology and cognitive science.

Joe Carella is the Assistant Dean for Executive Education at the University of Arizona . Joe has over 20 years of experience in helping executives and corporations in managing change and developing successful business strategies. His doctoral research and executive education engagements have seen him focus on corporate strategy, decision making and business performance with a variety of corporate clients including Hershey’s, Chevron, Fender Musical Instruments Corporation, Intel, DP World, Essilor, BBVA Compass Bank.

He explains some of the basic psychology behind problem solving: “When our brain is engaged in the process of solving problems, it is engaged in a series of steps where it processes and organizes the information it receives while developing new knowledge it uses in future steps. Creativity is embedded in this process by incorporating diverse inputs and/or new ways of organizing the information received.”

Laura MacLeod is a Professor of Social Group Work at City University of New York, and the creator of From The Inside Out Project® , a program that coaches managers in team leadership for a variety of workplaces. She has a background in social work and over two decades of experience as a union worker, and currently leads talks on conflict resolution, problem solving, and listening skills at conferences across the country.

MacLeod thinks of problem solving as an integral practice of successful organizations. “Problem solving is a collaborative process — all voices are heard and connected, and resolution is reached by the group,” she says. “Problems and conflicts occur in all groups and teams in the workplace, but if leaders involve everyone in working through, they will foster cohesion, engagement, and buy in. Everybody wins.”

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What Is the First Step in Solving a Problem?

Although problem solving techniques vary procedurally, experts agree that the first step in solving a problem is defining the problem. Without a clear articulation of the problem at stake, it is impossible to analyze all the key factors and actors, generate possible solutions, and then evaluate them to pick the best option.

Dr. Elliott Jaffa is a behavioral and management psychologist with over 25 years of problem solving training and management experience. “Start with defining the problem you want to solve,” he says, “And then define where you want to be, what you want to come away with.” He emphasizes these are the first steps in creating an actionable, clear solution.

Bryan Mattimore is Co-Founder of Growth Engine, an 18-year old innovation agency based in Norwalk, CT. Bryan has facilitated over 1,000 ideation sessions and managed over 200 successful innovation projects leading to over $3 billion in new sales. His newest book is 21 Days to a Big Idea . When asked about the first critical component to successful problem solving, Mattimore says, “Defining the challenge correctly, or ‘solving the right problem’ … The three creative techniques we use to help our clients ‘identify the right problem to be solved’ are questioning assumptions, 20 questions, and problem redefinition. A good example of this was a new product challenge from a client to help them ‘invent a new iron. We got them to redefine the challenge as first: a) inventing new anti-wrinkle devices, and then b) inventing new garment care devices.”

What Are Problem Solving Skills?

To understand the necessary skills in problem solving, you should first understand the types of thinking often associated with strong decision making. Most problem solving techniques look for a balance between the following binaries:

Convergent vs. Divergent Thinking: Convergent thinking is bringing together disparate information or ideas to determine a single best answer or solution. This thinking style values logic, speed, and accuracy, and leaves no chance for ambiguity. Divergent thinking is focused on generating new ideas to identify and evaluate multiple possible solutions, often uniting ideas in unexpected combinations. Divergent thinking is characterized by creativity, complexity, curiosity, flexibility, originality, and risk-taking.
Pragmatics vs. Semantics: Pragmatics refer to the logic of the problem at hand, and semantics is how you interpret the problem to solve it. Both are important to yield the best possible solution.
Mathematical vs. Personal Problem Solving: Mathematical problem solving involves logic (usually leading to a single correct answer), and is useful for problems that involve numbers or require an objective, clear-cut solution. However, many workplace problems also require personal problem solving, which includes interpersonal, collaborative, and emotional intuition and skills.

The following basic methods are fundamental problem solving concepts. Implement them to help balance the above thinking models.

Reproductive Thinking: Reproductive thinking uses past experience to solve a problem. However, be careful not to rely too heavily on past solutions, and to evaluate current problems individually, with their own factors and parameters.
Idea Generation: The process of generating many possible courses of action to identify a solution. This is most commonly a team exercise because putting everyone’s ideas on the table will yield the greatest number of potential solutions.

However, many of the most critical problem solving skills are “soft” skills: personal and interpersonal understanding, intuitiveness, and strong listening.

Mattimore expands on this idea: “The seven key skills to be an effective creative problem solver that I detail in my book Idea Stormers: How to Lead and Inspire Creative Breakthroughs are: 1) curiosity 2) openness 3) a willingness to embrace ambiguity 4) the ability to identify and transfer principles across categories and disciplines 5) the desire to search for integrity in ideas, 6) the ability to trust and exercise “knowingness” and 7) the ability to envision new worlds (think Dr. Seuss, Star Wars, Hunger Games, Harry Potter, etc.).”

“As an individual contributor to problem solving it is important to exercise our curiosity, questioning, and visioning abilities,” advises Carella. “As a facilitator it is essential to allow for diverse ideas to emerge, be able to synthesize and ‘translate’ other people’s thinking, and build an extensive network of available resources.”

MacLeod says the following interpersonal skills are necessary to effectively facilitate group problem solving: “The abilities to invite participation (hear all voices, encourage silent members), not take sides, manage dynamics between the monopolizer, the scapegoat, and the bully, and deal with conflict (not avoiding it or shutting down).”

Furthermore, Jaffa explains that the skills of a strong problem solver aren’t measurable. The best way to become a creative problem solver, he says, is to do regular creative exercises that keep you sharp and force you to think outside the box. Carella echoes this sentiment: “Neuroscience tells us that creativity comes from creating novel neural paths. Allow a few minutes each day to exercise your brain with novel techniques and brain ‘tricks’ – read something new, drive to work via a different route, count backwards, smell a new fragrance, etc.”

What Is Creative Problem Solving? History, Evolution, and Core Principles

Creative problem solving (CPS) is a method of problem solving in which you approach a problem or challenge in an imaginative, innovative way. The goal of CPS is to come up with innovative solutions, make a decision, and take action quickly. Sidney Parnes and Alex Osborn are credited with developing the creative problem solving process in the 1950s. The concept was further studied and developed at SUNY Buffalo State and the Creative Education Foundation.

The core principles of CPS include the following:

Balance divergent and convergent thinking
Ask problems as questions
Defer or suspend judgement
Focus on “Yes, and…” rather than “No, but…”

According to Carella, “Creative problem solving is the mental process used for generating innovative and imaginative ideas as a solution to a problem or a challenge. Creative problem solving techniques can be pursued by individuals or groups.”

When asked to define CPS, Jaffa explains that it is, by nature, difficult to create boundaries for. “Creative problem solving is not cut and dry,” he says, “If you ask 100 different people the definition of creative problem solving, you’ll get 100 different responses - it’s a non-entity.”

Business presents a unique need for creative problem solving. Especially in today’s competitive landscape, organizations need to iterate quickly, innovate with intention, and constantly be at the cutting-edge of creativity and new ideas to succeed. Developing CPS skills among your workforce not only enables you to make faster, stronger in-the-moment decisions, but also inspires a culture of collaborative work and knowledge sharing. When people work together to generate multiple novel ideas and evaluate solutions, they are also more likely to arrive at an effective decision, which will improve business processes and reduce waste over time. In fact, CPS is so important that some companies now list creative problem solving skills as a job criteria.

MacLeod reiterates the vitality of creative problem solving in the workplace. “Problem solving is crucial for all groups and teams,” she says. “Leaders need to know how to guide the process, hear all voices and involve all members - it’s not easy.”

“This mental process [of CPS] is especially helpful in work environments where individuals and teams continuously struggle with new problems and challenges posed by their continuously changing environment,” adds Carella.

Problem Solving Best Practices

By nature, creative problem solving does not have a clear-cut set of do’s and don’ts. Rather, creating a culture of strong creative problem solvers requires flexibility, adaptation, and interpersonal skills. However, there are a several best practices that you should incorporate:

Use a Systematic Approach: Regardless of the technique you use, choose a systematic method that satisfies your workplace conditions and constraints (time, resources, budget, etc.). Although you want to preserve creativity and openness to new ideas, maintaining a structured approach to the process will help you stay organized and focused.
View Problems as Opportunities: Rather than focusing on the negatives or giving up when you encounter barriers, treat problems as opportunities to enact positive change on the situation. In fact, some experts even recommend defining problems as opportunities, to remain proactive and positive.
Change Perspective: Remember that there are multiple ways to solve any problem. If you feel stuck, changing perspective can help generate fresh ideas. A perspective change might entail seeking advice of a mentor or expert, understanding the context of a situation, or taking a break and returning to the problem later. “A sterile or familiar environment can stifle new thinking and new perspectives,” says Carella. “Make sure you get out to draw inspiration from spaces and people out of your usual reach.”
Break Down Silos: To invite the greatest possible number of perspectives to any problem, encourage teams to work cross-departmentally. This not only combines diverse expertise, but also creates a more trusting and collaborative environment, which is essential to effective CPS. According to Carella, “Big challenges are always best tackled by a group of people rather than left to a single individual. Make sure you create a space where the team can concentrate and convene.”
Employ Strong Leadership or a Facilitator: Some companies choose to hire an external facilitator that teaches problem solving techniques, best practices, and practicums to stimulate creative problem solving. But, internal managers and staff can also oversee these activities. Regardless of whether the facilitator is internal or external, choose a strong leader who will value others’ ideas and make space for creative solutions. Mattimore has specific advice regarding the role of a facilitator: “When facilitating, get the group to name a promising idea (it will crystalize the idea and make it more memorable), and facilitate deeper rather than broader. Push for not only ideas, but how an idea might specifically work, some of its possible benefits, who and when would be interested in an idea, etc. This fleshing-out process with a group will generate fewer ideas, but at the end of the day will yield more useful concepts that might be profitably pursued.” Additionally, Carella says that “Executives and managers don’t necessarily have to be creative problem solvers, but need to make sure that their teams are equipped with the right tools and resources to make this happen. Also they need to be able to foster an environment where failing fast is accepted and celebrated.”
Evaluate Your Current Processes: This practice can help you unlock bottlenecks, and also identify gaps in your data and information management, both of which are common roots of business problems.

MacLeod offers the following additional advice, “Always get the facts. Don’t jump too quickly to a solution – working through [problems] takes time and patience.”

Mattimore also stresses that how you introduce creative problem solving is important. “Do not start by introducing a new company-wide innovation process,” he says. “Instead, encourage smaller teams to pursue specific creative projects, and then build a process from the ground up by emulating these smaller teams’ successful approaches. We say: ‘You don’t innovate by changing the culture, you change the culture by innovating.’”

Barriers to Effective Problem Solving

Learning how to effectively solve problems is difficult and takes time and continual adaptation. There are several common barriers to successful CPS, including:

Confirmation Bias: The tendency to only search for or interpret information that confirms a person’s existing ideas. People misinterpret or disregard data that doesn’t align with their beliefs.
Mental Set: People’s inclination to solve problems using the same tactics they have used to solve problems in the past. While this can sometimes be a useful strategy (see Analogical Thinking in a later section), it often limits inventiveness and creativity.
Functional Fixedness: This is another form of narrow thinking, where people become “stuck” thinking in a certain way and are unable to be flexible or change perspective.
Unnecessary Constraints: When people are overwhelmed with a problem, they can invent and impose additional limits on solution avenues. To avoid doing this, maintain a structured, level-headed approach to evaluating causes, effects, and potential solutions.
Groupthink: Be wary of the tendency for group members to agree with each other — this might be out of conflict avoidance, path of least resistance, or fear of speaking up. While this agreeableness might make meetings run smoothly, it can actually stunt creativity and idea generation, therefore limiting the success of your chosen solution.
Irrelevant Information: The tendency to pile on multiple problems and factors that may not even be related to the challenge at hand. This can cloud the team’s ability to find direct, targeted solutions.
Paradigm Blindness: This is found in people who are unwilling to adapt or change their worldview, outlook on a particular problem, or typical way of processing information. This can erode the effectiveness of problem solving techniques because they are not aware of the narrowness of their thinking, and therefore cannot think or act outside of their comfort zone.

According to Jaffa, the primary barrier of effective problem solving is rigidity. “The most common things people say are, ‘We’ve never done it before,’ or ‘We’ve always done it this way.’” While these feelings are natural, Jaffa explains that this rigid thinking actually precludes teams from identifying creative, inventive solutions that result in the greatest benefit.

“The biggest barrier to creative problem solving is a lack of awareness – and commitment to – training employees in state-of-the-art creative problem-solving techniques,” Mattimore explains. “We teach our clients how to use ideation techniques (as many as two-dozen different creative thinking techniques) to help them generate more and better ideas. Ideation techniques use specific and customized stimuli, or ‘thought triggers’ to inspire new thinking and new ideas.”

MacLeod adds that ineffective or rushed leadership is another common culprit. “We're always in a rush to fix quickly,” she says. “Sometimes leaders just solve problems themselves, making unilateral decisions to save time. But the investment is well worth it — leaders will have less on their plates if they can teach and eventually trust the team to resolve. Teams feel empowered and engagement and investment increases.”

Strategies for Problem Cause Identification

As discussed, most experts agree that the first and most crucial step in problem solving is defining the problem. Once you’ve done this, however, it may not be appropriate to move straight to the solution phase. Rather, it is often helpful to identify the cause(s) of the problem: This will better inform your solution planning and execution, and help ensure that you don’t fall victim to the same challenges in the future.

Below are some of the most common strategies for identifying the cause of a problem:

Root Cause Analysis: This method helps identify the most critical cause of a problem. A factor is considered a root cause if removing it prevents the problem from recurring. Performing a root cause analysis is a 12 step process that includes: define the problem, gather data on the factors contributing to the problem, group the factors based on shared characteristics, and create a cause-and-effect timeline to determine the root cause. After that, you identify and evaluate corrective actions to eliminate the root cause.

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Problem Solving Techniques and Strategies

In this section, we’ll explain several traditional and creative problem solving methods that you can use to identify challenges, create actionable goals, and resolve problems as they arise. Although there is often procedural and objective crossover among techniques, they are grouped by theme so you can identify which method works best for your organization.

Divergent Creative Problem Solving Techniques

Brainstorming: One of the most common methods of divergent thinking, brainstorming works best in an open group setting where everyone is encouraged to share their creative ideas. The goal is to generate as many ideas as possible – you analyze, critique, and evaluate the ideas only after the brainstorming session is complete. To learn more specific brainstorming techniques, read this article .

Mind Mapping: This is a visual thinking tool where you graphically depict concepts and their relation to one another. You can use mind mapping to structure the information you have, analyze and synthesize it, and generate solutions and new ideas from there. The goal of a mind map is to simplify complicated problems so you can more clearly identify solutions.

Appreciative Inquiry (AI): The basic assumption of AI is that “an organization is a mystery to be embraced.” Using this principle, AI takes a positive, inquisitive approach to identifying the problem, analyzing the causes, and presenting possible solutions. The five principles of AI emphasize dialogue, deliberate language and outlook, and social bonding.

Lateral Thinking: This is an indirect problem solving approach centered on the momentum of idea generation. As opposed to critical thinking, where people value ideas based on their truth and the absence of errors, lateral thinking values the “movement value” of new ideas: This means that you reward team members for producing a large volume of new ideas rapidly. With this approach, you’ll generate many new ideas before approving or rejecting any.

Problem Solving Techniques to Change Perspective

Constructive Controversy: This is a structured approach to group decision making to preserve critical thinking and disagreement while maintaining order. After defining the problem and presenting multiple courses of action, the group divides into small advocacy teams who research, analyze, and refute a particular option. Once each advocacy team has presented its best-case scenario, the group has a discussion (advocacy teams still defend their presented idea). Arguing and playing devil’s advocate is encouraged to reach an understanding of the pros and cons of each option. Next, advocacy teams abandon their cause and evaluate the options openly until they reach a consensus. All team members formally commit to the decision, regardless of whether they advocated for it at the beginning. You can learn more about the goals and steps in constructive controversy here .

Carella is a fan of this approach. “Create constructive controversy by having two teams argue the pros and cons of a certain idea,” he says. “It forces unconscious biases to surface and gives space for new ideas to formulate.”

Abstraction: In this method, you apply the problem to a fictional model of the current situation. Mapping an issue to an abstract situation can shed extraneous or irrelevant factors, and reveal places where you are overlooking obvious solutions or becoming bogged down by circumstances.

Analogical Thinking: Also called analogical reasoning , this method relies on an analogy: using information from one problem to solve another problem (these separate problems are called domains). It can be difficult for teams to create analogies among unrelated problems, but it is a strong technique to help you identify repeated issues, zoom out and change perspective, and prevent the problems from occurring in the future. .

CATWOE: This framework ensures that you evaluate the perspectives of those whom your decision will impact. The factors and questions to consider include (which combine to make the acronym CATWOE):

Customers: Who is on the receiving end of your decisions? What problem do they currently have, and how will they react to your proposed solution?
Actors: Who is acting to bring your solution to fruition? How will they respond and be affected by your decision?
Transformation Process: What processes will you employ to transform your current situation and meet your goals? What are the inputs and outputs?
World View: What is the larger context of your proposed solution? What is the larger, big-picture problem you are addressing?
Owner: Who actually owns the process? How might they influence your proposed solution (positively or negatively), and how can you influence them to help you?
Environmental Constraints: What are the limits (environmental, resource- and budget-wise, ethical, legal, etc.) on your ideas? How will you revise or work around these constraints?

Complex Problem Solving

Soft Systems Methodology (SSM): For extremely complex problems, SSM can help you identify how factors interact, and determine the best course of action. SSM was borne out of organizational process modeling and general systems theory, which hold that everything is part of a greater, interconnected system: This idea works well for “hard” problems (where logic and a single correct answer are prioritized), and less so for “soft” problems (i.e., human problems where factors such as personality, emotions, and hierarchy come into play). Therefore, SSM defines a seven step process for problem solving:

Begin with the problem or problematic situation
Express the problem or situation and build a rich picture of the themes of the problem
Identify the root causes of the problem (most commonly with CATWOE)
Build conceptual models of human activity surrounding the problem or situation
Compare models with real-world happenings
Identify changes to the situation that are both feasible and desirable
Take action to implement changes and improve the problematic situation

SSM can be used for any complex soft problem, and is also a useful tool in change management .

Failure Mode and Effects Analysis (FMEA): This method helps teams anticipate potential problems and take steps to mitigate them. Use FMEA when you are designing (redesigning) a complex function, process, product, or service. First, identify the failure modes, which are the possible ways that a project could fail. Then, perform an effects analysis to understand the consequences of each of the potential downfalls. This exercise is useful for internalizing the severity of each potential failure and its effects so you can make adjustments or safeties in your plan.

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Problem Solving Based on Data or Logic (Heuristic Methods)

TRIZ: A Russian-developed problem solving technique that values logic, analysis, and forecasting over intuition or soft reasoning. TRIZ (translated to “theory of inventive problem solving” or TIPS in English) is a systematic approach to defining and identifying an inventive solution to difficult problems. The method offers several strategies for arriving at an inventive solution, including a contradictions matrix to assess trade-offs among solutions, a Su-Field analysis which uses formulas to describe a system by its structure, and ARIZ (algorithm of inventive problem solving) which uses algorithms to find inventive solutions.

Inductive Reasoning: A logical method that uses evidence to conclude that a certain answer is probable (this is opposed to deductive reasoning, where the answer is assumed to be true). Inductive reasoning uses a limited number of observations to make useful, logical conclusions (for example, the Scientific Method is an extreme example of inductive reasoning). However, this method doesn’t always map well to human problems in the workplace — in these instances, managers should employ intuitive inductive reasoning , which allows for more automatic, implicit conclusions so that work can progress. This, of course, retains the principle that these intuitive conclusions are not necessarily the one and only correct answer.

Process-Oriented Problem Solving Methods

Plan Do Check Act (PDCA): This is an iterative management technique used to ensure continual improvement of products or processes. First, teams plan (establish objectives to meet desired end results), then do (implement the plan, new processes, or produce the output), then check (compare expected with actual results), and finally act (define how the organization will act in the future, based on the performance and knowledge gained in the previous three steps).

Means-End Analysis (MEA): The MEA strategy is to reduce the difference between the current (problematic) state and the goal state. To do so, teams compile information on the multiple factors that contribute to the disparity between the current and goal states. Then they try to change or eliminate the factors one by one, beginning with the factor responsible for the greatest difference in current and goal state. By systematically tackling the multiple factors that cause disparity between the problem and desired outcome, teams can better focus energy and control each step of the process.

Hurson’s Productive Thinking Model: This technique was developed by Tim Hurson, and is detailed in his 2007 book Think Better: An Innovator’s Guide to Productive Thinking . The model outlines six steps that are meant to give structure while maintaining creativity and critical thinking: 1) Ask “What is going on?” 2) Ask “What is success?” 3) Ask “What is the question?” 4) Generate answers 5) Forge the solution 6) Align resources.

Control Influence Accept (CIA): The basic premise of CIA is that how you respond to problems determines how successful you will be in overcoming them. Therefore, this model is both a problem solving technique and stress-management tool that ensures you aren’t responding to problems in a reactive and unproductive way. The steps in CIA include:

Control: Identify the aspects of the problem that are within your control.
Influence: Identify the aspects of the problem that you cannot control, but that you can influence.
Accept: Identify the aspects of the problem that you can neither control nor influence, and react based on this composite information.

GROW Model: This is a straightforward problem solving method for goal setting that clearly defines your goals and current situation, and then asks you to define the potential solutions and be realistic about your chosen course of action. The steps break down as follows:

Goal: What do you want?
Reality: Where are you now?
Options: What could you do?
Will: What will you do?

OODA Loop: This acronym stands for observe, orient, decide, and act. This approach is a decision-making cycle that values agility and flexibility over raw human force. It is framed as a loop because of the understanding that any team will continually encounter problems or opponents to success and have to overcome them.

There are also many un-named creative problem solving techniques that follow a sequenced series of steps. While the exact steps vary slightly, they all follow a similar trajectory and aim to accomplish similar goals of problem, cause, and goal identification, idea generation, and active solution implementation.

MacLeod offers her own problem solving procedure, which echoes the above steps:

“1. Recognize the Problem: State what you see. Sometimes the problem is covert. 2. Identify: Get the facts — What exactly happened? What is the issue? 3. and 4. Explore and Connect: Dig deeper and encourage group members to relate their similar experiences. Now you're getting more into the feelings and background [of the situation], not just the facts. 5. Possible Solutions: Consider and brainstorm ideas for resolution. 6. Implement: Choose a solution and try it out — this could be role play and/or a discussion of how the solution would be put in place. 7. Evaluate: Revisit to see if the solution was successful or not.”

Many of these problem solving techniques can be used in concert with one another, or multiple can be appropriate for any given problem. It’s less about facilitating a perfect CPS session, and more about encouraging team members to continually think outside the box and push beyond personal boundaries that inhibit their innovative thinking. So, try out several methods, find those that resonate best with your team, and continue adopting new techniques and adapting your processes along the way.

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How to master the seven-step problem-solving process

In this episode of the McKinsey Podcast , Simon London speaks with Charles Conn, CEO of venture-capital firm Oxford Sciences Innovation, and McKinsey senior partner Hugo Sarrazin about the complexities of different problem-solving strategies.

Podcast transcript

Simon London: Hello, and welcome to this episode of the McKinsey Podcast , with me, Simon London. What’s the number-one skill you need to succeed professionally? Salesmanship, perhaps? Or a facility with statistics? Or maybe the ability to communicate crisply and clearly? Many would argue that at the very top of the list comes problem solving: that is, the ability to think through and come up with an optimal course of action to address any complex challenge—in business, in public policy, or indeed in life.

Looked at this way, it’s no surprise that McKinsey takes problem solving very seriously, testing for it during the recruiting process and then honing it, in McKinsey consultants, through immersion in a structured seven-step method. To discuss the art of problem solving, I sat down in California with McKinsey senior partner Hugo Sarrazin and also with Charles Conn. Charles is a former McKinsey partner, entrepreneur, executive, and coauthor of the book Bulletproof Problem Solving: The One Skill That Changes Everything [John Wiley & Sons, 2018].

Charles and Hugo, welcome to the podcast. Thank you for being here.

Hugo Sarrazin: Our pleasure.

Charles Conn: It’s terrific to be here.

Simon London: Problem solving is a really interesting piece of terminology. It could mean so many different things. I have a son who’s a teenage climber. They talk about solving problems. Climbing is problem solving. Charles, when you talk about problem solving, what are you talking about?

Charles Conn: For me, problem solving is the answer to the question “What should I do?” It’s interesting when there’s uncertainty and complexity, and when it’s meaningful because there are consequences. Your son’s climbing is a perfect example. There are consequences, and it’s complicated, and there’s uncertainty—can he make that grab? I think we can apply that same frame almost at any level. You can think about questions like “What town would I like to live in?” or “Should I put solar panels on my roof?”

You might think that’s a funny thing to apply problem solving to, but in my mind it’s not fundamentally different from business problem solving, which answers the question “What should my strategy be?” Or problem solving at the policy level: “How do we combat climate change?” “Should I support the local school bond?” I think these are all part and parcel of the same type of question, “What should I do?”

I’m a big fan of structured problem solving. By following steps, we can more clearly understand what problem it is we’re solving, what are the components of the problem that we’re solving, which components are the most important ones for us to pay attention to, which analytic techniques we should apply to those, and how we can synthesize what we’ve learned back into a compelling story. That’s all it is, at its heart.

I think sometimes when people think about seven steps, they assume that there’s a rigidity to this. That’s not it at all. It’s actually to give you the scope for creativity, which often doesn’t exist when your problem solving is muddled.

Simon London: You were just talking about the seven-step process. That’s what’s written down in the book, but it’s a very McKinsey process as well. Without getting too deep into the weeds, let’s go through the steps, one by one. You were just talking about problem definition as being a particularly important thing to get right first. That’s the first step. Hugo, tell us about that.

Hugo Sarrazin: It is surprising how often people jump past this step and make a bunch of assumptions. The most powerful thing is to step back and ask the basic questions—“What are we trying to solve? What are the constraints that exist? What are the dependencies?” Let’s make those explicit and really push the thinking and defining. At McKinsey, we spend an enormous amount of time in writing that little statement, and the statement, if you’re a logic purist, is great. You debate. “Is it an ‘or’? Is it an ‘and’? What’s the action verb?” Because all these specific words help you get to the heart of what matters.

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Simon London: So this is a concise problem statement.

Hugo Sarrazin: Yeah. It’s not like “Can we grow in Japan?” That’s interesting, but it is “What, specifically, are we trying to uncover in the growth of a product in Japan? Or a segment in Japan? Or a channel in Japan?” When you spend an enormous amount of time, in the first meeting of the different stakeholders, debating this and having different people put forward what they think the problem definition is, you realize that people have completely different views of why they’re here. That, to me, is the most important step.

Charles Conn: I would agree with that. For me, the problem context is critical. When we understand “What are the forces acting upon your decision maker? How quickly is the answer needed? With what precision is the answer needed? Are there areas that are off limits or areas where we would particularly like to find our solution? Is the decision maker open to exploring other areas?” then you not only become more efficient, and move toward what we call the critical path in problem solving, but you also make it so much more likely that you’re not going to waste your time or your decision maker’s time.

How often do especially bright young people run off with half of the idea about what the problem is and start collecting data and start building models—only to discover that they’ve really gone off half-cocked.

Hugo Sarrazin: Yeah.

Charles Conn: And in the wrong direction.

Simon London: OK. So step one—and there is a real art and a structure to it—is define the problem. Step two, Charles?

Charles Conn: My favorite step is step two, which is to use logic trees to disaggregate the problem. Every problem we’re solving has some complexity and some uncertainty in it. The only way that we can really get our team working on the problem is to take the problem apart into logical pieces.

What we find, of course, is that the way to disaggregate the problem often gives you an insight into the answer to the problem quite quickly. I love to do two or three different cuts at it, each one giving a bit of a different insight into what might be going wrong. By doing sensible disaggregations, using logic trees, we can figure out which parts of the problem we should be looking at, and we can assign those different parts to team members.

Simon London: What’s a good example of a logic tree on a sort of ratable problem?

Charles Conn: Maybe the easiest one is the classic profit tree. Almost in every business that I would take a look at, I would start with a profit or return-on-assets tree. In its simplest form, you have the components of revenue, which are price and quantity, and the components of cost, which are cost and quantity. Each of those can be broken out. Cost can be broken into variable cost and fixed cost. The components of price can be broken into what your pricing scheme is. That simple tree often provides insight into what’s going on in a business or what the difference is between that business and the competitors.

If we add the leg, which is “What’s the asset base or investment element?”—so profit divided by assets—then we can ask the question “Is the business using its investments sensibly?” whether that’s in stores or in manufacturing or in transportation assets. I hope we can see just how simple this is, even though we’re describing it in words.

When I went to work with Gordon Moore at the Moore Foundation, the problem that he asked us to look at was “How can we save Pacific salmon?” Now, that sounds like an impossible question, but it was amenable to precisely the same type of disaggregation and allowed us to organize what became a 15-year effort to improve the likelihood of good outcomes for Pacific salmon.

Simon London: Now, is there a danger that your logic tree can be impossibly large? This, I think, brings us onto the third step in the process, which is that you have to prioritize.

Charles Conn: Absolutely. The third step, which we also emphasize, along with good problem definition, is rigorous prioritization—we ask the questions “How important is this lever or this branch of the tree in the overall outcome that we seek to achieve? How much can I move that lever?” Obviously, we try and focus our efforts on ones that have a big impact on the problem and the ones that we have the ability to change. With salmon, ocean conditions turned out to be a big lever, but not one that we could adjust. We focused our attention on fish habitats and fish-harvesting practices, which were big levers that we could affect.

People spend a lot of time arguing about branches that are either not important or that none of us can change. We see it in the public square. When we deal with questions at the policy level—“Should you support the death penalty?” “How do we affect climate change?” “How can we uncover the causes and address homelessness?”—it’s even more important that we’re focusing on levers that are big and movable.

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Simon London: Let’s move swiftly on to step four. You’ve defined your problem, you disaggregate it, you prioritize where you want to analyze—what you want to really look at hard. Then you got to the work plan. Now, what does that mean in practice?

Hugo Sarrazin: Depending on what you’ve prioritized, there are many things you could do. It could be breaking the work among the team members so that people have a clear piece of the work to do. It could be defining the specific analyses that need to get done and executed, and being clear on time lines. There’s always a level-one answer, there’s a level-two answer, there’s a level-three answer. Without being too flippant, I can solve any problem during a good dinner with wine. It won’t have a whole lot of backing.

Simon London: Not going to have a lot of depth to it.

Hugo Sarrazin: No, but it may be useful as a starting point. If the stakes are not that high, that could be OK. If it’s really high stakes, you may need level three and have the whole model validated in three different ways. You need to find a work plan that reflects the level of precision, the time frame you have, and the stakeholders you need to bring along in the exercise.

Charles Conn: I love the way you’ve described that, because, again, some people think of problem solving as a linear thing, but of course what’s critical is that it’s iterative. As you say, you can solve the problem in one day or even one hour.

Charles Conn: We encourage our teams everywhere to do that. We call it the one-day answer or the one-hour answer. In work planning, we’re always iterating. Every time you see a 50-page work plan that stretches out to three months, you know it’s wrong. It will be outmoded very quickly by that learning process that you described. Iterative problem solving is a critical part of this. Sometimes, people think work planning sounds dull, but it isn’t. It’s how we know what’s expected of us and when we need to deliver it and how we’re progressing toward the answer. It’s also the place where we can deal with biases. Bias is a feature of every human decision-making process. If we design our team interactions intelligently, we can avoid the worst sort of biases.

Simon London: Here we’re talking about cognitive biases primarily, right? It’s not that I’m biased against you because of your accent or something. These are the cognitive biases that behavioral sciences have shown we all carry around, things like anchoring, overoptimism—these kinds of things.

Both: Yeah.

Charles Conn: Availability bias is the one that I’m always alert to. You think you’ve seen the problem before, and therefore what’s available is your previous conception of it—and we have to be most careful about that. In any human setting, we also have to be careful about biases that are based on hierarchies, sometimes called sunflower bias. I’m sure, Hugo, with your teams, you make sure that the youngest team members speak first. Not the oldest team members, because it’s easy for people to look at who’s senior and alter their own creative approaches.

Hugo Sarrazin: It’s helpful, at that moment—if someone is asserting a point of view—to ask the question “This was true in what context?” You’re trying to apply something that worked in one context to a different one. That can be deadly if the context has changed, and that’s why organizations struggle to change. You promote all these people because they did something that worked well in the past, and then there’s a disruption in the industry, and they keep doing what got them promoted even though the context has changed.

Simon London: Right. Right.

Hugo Sarrazin: So it’s the same thing in problem solving.

Charles Conn: And it’s why diversity in our teams is so important. It’s one of the best things about the world that we’re in now. We’re likely to have people from different socioeconomic, ethnic, and national backgrounds, each of whom sees problems from a slightly different perspective. It is therefore much more likely that the team will uncover a truly creative and clever approach to problem solving.

Simon London: Let’s move on to step five. You’ve done your work plan. Now you’ve actually got to do the analysis. The thing that strikes me here is that the range of tools that we have at our disposal now, of course, is just huge, particularly with advances in computation, advanced analytics. There’s so many things that you can apply here. Just talk about the analysis stage. How do you pick the right tools?

Charles Conn: For me, the most important thing is that we start with simple heuristics and explanatory statistics before we go off and use the big-gun tools. We need to understand the shape and scope of our problem before we start applying these massive and complex analytical approaches.

Simon London: Would you agree with that?

Hugo Sarrazin: I agree. I think there are so many wonderful heuristics. You need to start there before you go deep into the modeling exercise. There’s an interesting dynamic that’s happening, though. In some cases, for some types of problems, it is even better to set yourself up to maximize your learning. Your problem-solving methodology is test and learn, test and learn, test and learn, and iterate. That is a heuristic in itself, the A/B testing that is used in many parts of the world. So that’s a problem-solving methodology. It’s nothing different. It just uses technology and feedback loops in a fast way. The other one is exploratory data analysis. When you’re dealing with a large-scale problem, and there’s so much data, I can get to the heuristics that Charles was talking about through very clever visualization of data.

You test with your data. You need to set up an environment to do so, but don’t get caught up in neural-network modeling immediately. You’re testing, you’re checking—“Is the data right? Is it sound? Does it make sense?”—before you launch too far.

Simon London: You do hear these ideas—that if you have a big enough data set and enough algorithms, they’re going to find things that you just wouldn’t have spotted, find solutions that maybe you wouldn’t have thought of. Does machine learning sort of revolutionize the problem-solving process? Or are these actually just other tools in the toolbox for structured problem solving?

Charles Conn: It can be revolutionary. There are some areas in which the pattern recognition of large data sets and good algorithms can help us see things that we otherwise couldn’t see. But I do think it’s terribly important we don’t think that this particular technique is a substitute for superb problem solving, starting with good problem definition. Many people use machine learning without understanding algorithms that themselves can have biases built into them. Just as 20 years ago, when we were doing statistical analysis, we knew that we needed good model definition, we still need a good understanding of our algorithms and really good problem definition before we launch off into big data sets and unknown algorithms.

Simon London: Step six. You’ve done your analysis.

Charles Conn: I take six and seven together, and this is the place where young problem solvers often make a mistake. They’ve got their analysis, and they assume that’s the answer, and of course it isn’t the answer. The ability to synthesize the pieces that came out of the analysis and begin to weave those into a story that helps people answer the question “What should I do?” This is back to where we started. If we can’t synthesize, and we can’t tell a story, then our decision maker can’t find the answer to “What should I do?”

Simon London: But, again, these final steps are about motivating people to action, right?

Charles Conn: Yeah.

Simon London: I am slightly torn about the nomenclature of problem solving because it’s on paper, right? Until you motivate people to action, you actually haven’t solved anything.

Charles Conn: I love this question because I think decision-making theory, without a bias to action, is a waste of time. Everything in how I approach this is to help people take action that makes the world better.

Simon London: Hence, these are absolutely critical steps. If you don’t do this well, you’ve just got a bunch of analysis.

Charles Conn: We end up in exactly the same place where we started, which is people speaking across each other, past each other in the public square, rather than actually working together, shoulder to shoulder, to crack these important problems.

Simon London: In the real world, we have a lot of uncertainty—arguably, increasing uncertainty. How do good problem solvers deal with that?

Hugo Sarrazin: At every step of the process. In the problem definition, when you’re defining the context, you need to understand those sources of uncertainty and whether they’re important or not important. It becomes important in the definition of the tree.

You need to think carefully about the branches of the tree that are more certain and less certain as you define them. They don’t have equal weight just because they’ve got equal space on the page. Then, when you’re prioritizing, your prioritization approach may put more emphasis on things that have low probability but huge impact—or, vice versa, may put a lot of priority on things that are very likely and, hopefully, have a reasonable impact. You can introduce that along the way. When you come back to the synthesis, you just need to be nuanced about what you’re understanding, the likelihood.

Often, people lack humility in the way they make their recommendations: “This is the answer.” They’re very precise, and I think we would all be well-served to say, “This is a likely answer under the following sets of conditions” and then make the level of uncertainty clearer, if that is appropriate. It doesn’t mean you’re always in the gray zone; it doesn’t mean you don’t have a point of view. It just means that you can be explicit about the certainty of your answer when you make that recommendation.

Simon London: So it sounds like there is an underlying principle: “Acknowledge and embrace the uncertainty. Don’t pretend that it isn’t there. Be very clear about what the uncertainties are up front, and then build that into every step of the process.”

Hugo Sarrazin: Every step of the process.

Simon London: Yeah. We have just walked through a particular structured methodology for problem solving. But, of course, this is not the only structured methodology for problem solving. One that is also very well-known is design thinking, which comes at things very differently. So, Hugo, I know you have worked with a lot of designers. Just give us a very quick summary. Design thinking—what is it, and how does it relate?

Hugo Sarrazin: It starts with an incredible amount of empathy for the user and uses that to define the problem. It does pause and go out in the wild and spend an enormous amount of time seeing how people interact with objects, seeing the experience they’re getting, seeing the pain points or joy—and uses that to infer and define the problem.

Simon London: Problem definition, but out in the world.

Hugo Sarrazin: With an enormous amount of empathy. There’s a huge emphasis on empathy. Traditional, more classic problem solving is you define the problem based on an understanding of the situation. This one almost presupposes that we don’t know the problem until we go see it. The second thing is you need to come up with multiple scenarios or answers or ideas or concepts, and there’s a lot of divergent thinking initially. That’s slightly different, versus the prioritization, but not for long. Eventually, you need to kind of say, “OK, I’m going to converge again.” Then you go and you bring things back to the customer and get feedback and iterate. Then you rinse and repeat, rinse and repeat. There’s a lot of tactile building, along the way, of prototypes and things like that. It’s very iterative.

Simon London: So, Charles, are these complements or are these alternatives?

Charles Conn: I think they’re entirely complementary, and I think Hugo’s description is perfect. When we do problem definition well in classic problem solving, we are demonstrating the kind of empathy, at the very beginning of our problem, that design thinking asks us to approach. When we ideate—and that’s very similar to the disaggregation, prioritization, and work-planning steps—we do precisely the same thing, and often we use contrasting teams, so that we do have divergent thinking. The best teams allow divergent thinking to bump them off whatever their initial biases in problem solving are. For me, design thinking gives us a constant reminder of creativity, empathy, and the tactile nature of problem solving, but it’s absolutely complementary, not alternative.

Simon London: I think, in a world of cross-functional teams, an interesting question is do people with design-thinking backgrounds really work well together with classical problem solvers? How do you make that chemistry happen?

Hugo Sarrazin: Yeah, it is not easy when people have spent an enormous amount of time seeped in design thinking or user-centric design, whichever word you want to use. If the person who’s applying classic problem-solving methodology is very rigid and mechanical in the way they’re doing it, there could be an enormous amount of tension. If there’s not clarity in the role and not clarity in the process, I think having the two together can be, sometimes, problematic.

The second thing that happens often is that the artifacts the two methodologies try to gravitate toward can be different. Classic problem solving often gravitates toward a model; design thinking migrates toward a prototype. Rather than writing a big deck with all my supporting evidence, they’ll bring an example, a thing, and that feels different. Then you spend your time differently to achieve those two end products, so that’s another source of friction.

Now, I still think it can be an incredibly powerful thing to have the two—if there are the right people with the right mind-set, if there is a team that is explicit about the roles, if we’re clear about the kind of outcomes we are attempting to bring forward. There’s an enormous amount of collaborativeness and respect.

Simon London: But they have to respect each other’s methodology and be prepared to flex, maybe, a little bit, in how this process is going to work.

Hugo Sarrazin: Absolutely.

Simon London: The other area where, it strikes me, there could be a little bit of a different sort of friction is this whole concept of the day-one answer, which is what we were just talking about in classical problem solving. Now, you know that this is probably not going to be your final answer, but that’s how you begin to structure the problem. Whereas I would imagine your design thinkers—no, they’re going off to do their ethnographic research and get out into the field, potentially for a long time, before they come back with at least an initial hypothesis.

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Hugo Sarrazin: That is a great callout, and that’s another difference. Designers typically will like to soak into the situation and avoid converging too quickly. There’s optionality and exploring different options. There’s a strong belief that keeps the solution space wide enough that you can come up with more radical ideas. If there’s a large design team or many designers on the team, and you come on Friday and say, “What’s our week-one answer?” they’re going to struggle. They’re not going to be comfortable, naturally, to give that answer. It doesn’t mean they don’t have an answer; it’s just not where they are in their thinking process.

Simon London: I think we are, sadly, out of time for today. But Charles and Hugo, thank you so much.

Charles Conn: It was a pleasure to be here, Simon.

Hugo Sarrazin: It was a pleasure. Thank you.

Simon London: And thanks, as always, to you, our listeners, for tuning into this episode of the McKinsey Podcast . If you want to learn more about problem solving, you can find the book, Bulletproof Problem Solving: The One Skill That Changes Everything , online or order it through your local bookstore. To learn more about McKinsey, you can of course find us at McKinsey.com.

Charles Conn is CEO of Oxford Sciences Innovation and an alumnus of McKinsey’s Sydney office. Hugo Sarrazin is a senior partner in the Silicon Valley office, where Simon London, a member of McKinsey Publishing, is also based.

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Problem-Solving Techniques and Tips (That Actually Work)

June 14, 2022 - 10 min read

Solving complex problems may be difficult but it doesn't have to be excruciating. You just need the right frame of mind and a process for untangling the problem at hand.

Luckily for you, there are plenty of techniques available to solve whatever problems come at you in the workplace.

When faced with a doozy of a problem, where do you start? And what problem-solving techniques can you use right now that can help you make good decisions?

Today's post will give you tips and techniques for solving complex problems so you can untangle any complication like an expert.

How many steps are there in problem-solving?

At its core, problem-solving is a methodical four-step process. You may even recall these steps from when you were first introduced to the Scientific Method.

First, you must define the problem . What is its cause? What are the signs there's a problem at all?
Next, you identify various options for solutions. What are some good ideas to solve this?
Then, evaluate your options and choose from among them. What is the best option to solve the problem? What's the easiest option? How should you prioritize?
Finally, implement the chosen solution . Does it solve the problem? Is there another option you need to try?

When applying problem-solving techniques, you will be using a variation of these steps as your foundation.

Takeaway: Before you can solve a problem, seek to understand it fully.

Creative problem-solving techniques

Time to get creative! You might think this will just be a list of out-of-the-box ways to brainstorm ideas. Not exactly.

Creative problem solving (CPS) is actually a formal process formulated by Sidney Parnes and Alex Faickney Osborn , who is thought of as the father of traditional brainstorming (and the "O" in famous advertising agency BBDO).

Their creative problem solving process emphasizes several things, namely:

Separate ideation from evaluation . When you brainstorm creative ideas, have a separate time for writing it all down. Focus on generating lots of ideas. Don't prioritize or evaluate them until everything is captured.
Judging will shut it down . Nothing stops the flow of creative ideas faster than judging them on the spot. Wait until the brainstorming is over before you evaluate.
Restate problems as questions . It's easier to entice a group into thinking of creative ideas when challenges are stated as open-ended questions.
Use "Yes and" to expand ideas . Here's one of the basic tenets of improv comedy. It's way too easy to shut down and negate ideas by using the word "but" (i.e. "But I think this is better..."). Avoid this at all costs. Instead, expand on what was previously introduced by saying "Yes, and..." to keep ideas flowing and evolving.

Takeaway: When brainstorming solutions, generate ideas first by using questions and building off of existing ideas. Do all evaluating and judging later.

Problem-solving tips from psychology

If you take a look at the history of problem-solving techniques in psychology, you'll come across a wide spectrum of interesting ideas that could be helpful.

Take it from experience

In 1911, the American psychologist Edward Thorndike observed cats figuring out how to escape from the cage he placed them in. From this, Thorndike developed his law of effect , which states: If you succeed via trial-and-error, you're more likely to use those same actions and ideas that led to your previous success when you face the problem again.

Takeaway: Your past experience can inform and shed light on the problem you face now. Recall. Explore.

Barriers to reproductive thinking

The Gestalt psychologists built on Thorndike's ideas when they proposed that problem-solving can happen via reproductive thinking — which is not about sex, but rather solving a problem by using past experience and reproducing that experience to solve the current problem.

What's interesting about Gestalt psychology is how they view barriers to problem-solving. Here are two such barriers:

Are you entrenched? Look up mental set or entrenchment . This is when you're fixated on a solution that used to work well in the past but has no bearing to your current problem. Are you so entrenched with a method or idea that you use it even when it doesn't work? As Queen Elsa sang, "Let it go!"
Are you thinking of alternative uses? There is a cognitive bias called functional fixedness which could thwart any of your critical thinking techniques by having you only see an object's conventional function. For example, say you need to cut a piece of paper in half but only have a ruler. Functional fixedness would lead you to think the ruler is only good for measuring things. (You could also use the ruler to crease the paper, making it easier to tear it in half.)

Takeaway: Think outside of the box! And by box, we mean outside of the past experience you're holding on to, or outside any preconceived ideas on how a tool is conventionally used.

Use a fishbone diagram to see cause and effect

The most important part of defining the problem is looking at the possible root cause. You'll need to ask yourself questions like: Where and when is it happening? How is it occurring? With whom is it happening? Why is it happening?

You can get to the root cause with a fishbone diagram (also known as an Ishikawa diagram or a cause and effect diagram).

Basically, you put the effect on the right side as the problem statement. Then you list all possible causes on the left, grouped into larger cause categories. The resulting shape resembles a fish skeleton. Which is a perfect way to say, "This problem smells fishy."

Fishbone diagram for cause and effect analysis - problem solving techniques

Use analogies to get to a solution

Analogical thinking uses information from one area to help with a problem in a different area. In short, solving a different problem can lead you to find a solution to the actual problem. Watch out though! Analogies are difficult for beginners and take some getting used to.

An example: In the "radiation problem," a doctor has a patient with a tumor that cannot be operated on. The doctor can use rays to destroy the tumor but it also destroys healthy tissue.

Two researchers, Gick and Holyoak , noted that people solved the radiation problem much more easily after being asked to read a story about an invading general who must capture the fortress of a king but be careful to avoid landmines that will detonate if large forces traverse the streets. The general then sends small forces of men down different streets so the army can converge at the fortress at the same time and can capture it at full force.

Ask "12 what elses"

In her book " The Architecture of All Abundance ," author Lenedra J. Carroll (aka the mother of pop star Jewel) talks about a question-and-answer technique for getting out of a problem.

When faced with a problem, ask yourself a question about it and brainstorm 12 answers ("12 what elses") to that problem. Then you can go further by taking one answer, turning it into a question and generating 12 more "what elses." Repeat until the solution is golden brown, fully baked, and ready to take out of the oven.

Start using these techniques today

Hopefully you find these different techniques useful and they get your imagination rolling with ideas on how to solve different problems.

And if that's the case, then you have four different takeaways to use the next time a problem gets you tangled up:

Don't start by trying to solve the problem. First, aim to understand the root of the problem.
Use questions to generate ideas for solving the problem.
Look to previous problems to find the answers to new ones.
Clear your preconceived ideas and past experiences before attempting to tackle the problem.

How to solve problems with Wrike

Empower your team to be even more productive with Wrike's project management and collaboration tools. With documents, revisions, and project -related communication all in one place, employees can use Wrike as a single source of truth for all project information.

Get 360-degree visibility of all your work and identify problems before they occur — see schedule or resource conflicts on Gantt charts, easily view progress with custom statuses, and move work along with automated approvals.

Want to streamline your processes and ease future problem-solving? Get started with a free two-week trial of Wrike today.

What are your favorite problem-solving techniques?

Do you have a problem-solving technique that has worked wonders for your organization? Hit the comments below and share your wisdom!

Lionel Valdellon

Lionel is a former Content Marketing Manager of Wrike. He is also a blogger since 1997, a productivity enthusiast, a project management newbie, a musician and producer of electronic downtempo music, a father of three, and a husband of one.

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36 Problem-solving techniques, methods and tools

When it comes to solving problems, getting ideas is the easy part.

But businesses often forget the other four stages of the problem-solving process that will allow them to find the best solution.

Instead of jumping straight to idea generation, your problem-solving framework should look like this:

Identify the problem
Reveal why it has occurred
Brainstorm ideas
Select the best solution

See how idea generation doesn’t appear until stage 3?!

In this extensive resource, we provide techniques, methodologies and tools to guide you through every stage of the problem-solving process.

Once you’ve finished reading, you’ll possess an extensive problem-solving arsenal that will enable you to overcome your biggest workplace challenges.

11 Problem-solving techniques for clarity and confidence

Before we dive into more comprehensive methodologies for solving problems, there are a few basic techniques you should know.

The following techniques will set you up for a successful problem-solving session with your team, allowing you to take on your biggest challenges with clarity and confidence. ‍

1. Take a moment, take a breath

When a problem or challenge arises, it’s normal to act too quickly or rely on solutions that have worked well in the past. This is known as entrenched thinking.

But acting impulsively, without prior consideration or planning, can cause you to misunderstand the issue and overlook possible solutions to the problem.

Therefore, the first thing you should always do when you encounter a problem is: breathe in and out.

Take a step back and make a clear plan of action before you act. This will help you to take rational steps towards solving a problem. ‍

2. Ask questions to understand the full extent of the issue

Another common mistake people make when attempting to solve a problem is taking action before fully understanding the problem.

Before committing to a theory, ask enough questions to unearth the true root of the issue.

Later in this article, we cover The 5 Why’s problem-solving methodology which you can use to easily identify the root of your problem. Give this a go at your next meeting and see how your initial understanding of a problem can often be wrong. ‍

3. Consider alternative perspectives

A common problem-solving issue is that of myopia—a narrow-minded view or perception of the problem. Myopia can occur when you’re too involved with the problem or your team isn’t diverse enough.

To give yourself the best chance of resolving a problem, gain insight from a wide range of sources. Collaborate with key stakeholders, customers and on-the-ground employees to learn how the problem affects them and whether they have found workarounds or solutions.

To paint the broadest picture, don’t limit your problem-solving team to a specific archetype. Try to include everyone, from the chief executive to the office janitor.

If you’re working with a small team, try the Flip It! problem-solving methodology to view the issue from a fresh angle. ‍

4. Make your office space conducive to problem-solving

The environment in which your host your brainstorming sessions should maximise creativity . When your team members trust each other and feel relaxed, they’re more likely to come up with innovative ideas and solutions to a problem.

Here are a few ways to get your employees’ creative juices flowing:

Play team-building games that maximise trust and build interpersonal relationships
Improve your team’s problem-solving skills with games that encourage critical thinking
Redesign the office with comfortable furniture and collaborative spaces
Boost job satisfaction by creating a positive work-life balance
Improve collaborative skills and learn to resolve conflicts

World Café is a problem-solving method that creates a casual environment conducive to creative thinking.

Keep reading to learn more about how World Café can help your team solve complex organisational problems. ‍

5. Use problem-solving methodologies to guide the process

Because problem-solving is a creative process, it can be hard to keep it on track. As more ideas get banded around, conflicts can arise that derail the session.

That’s why problem-solving methodologies are so helpful. They offer you proven problem-solving frameworks to guide your group sessions and keep them on track.

The Six Thinking Hats problem-solving method is a popular technique that guides the process and helps your team analyse a problem from all angles.

We’re going to take a look at our favourite problem-solving methodologies in the next section of this article, XY Tried and tested problem-solving methodologies. ‍

6. Use analogies to solve complex problems

Sometimes, solving a different problem can help you uncover solutions to another problem!

By stripping back a complex issue and framing it as a simplified analogy , you approach a problem from a different angle, enabling you to come up with alternative ideas.

After solving practice problems, your team might be more aptly equipped to solve real-world issues.

However, coming up with an analogy that reflects your issue can be difficult, so don’t worry if this technique doesn’t work for you.

The Speed Boat diagram is a visual tool that helps your employees view existing challenges as anchors holding back a boat which represents your end goals. By assigning a “weight” to each anchor, your team can prioritise which issues to tackle first. ‍

7. Establish clear constraints

Constraints make a big problem more approachable.

Before you tackle a problem, establish clear boundaries and codes of conduct for the session. This allows your team to focus on the current issue without becoming distracted or veering off on a tangent.

In an article published in the Harvard Business Review, authors Oguz A. Acar, Murat Tarakci, and Daan van Knippenberg wrote, “Constraints … provide focus and a creative challenge that motivates people to search for and connect information from different sources to generate novel ideas for new products, services, or business processes.” (Why Constraints Are Good for Innovation, 2019)

Lightning Decision Jam is a prime example of how constraints can assist the creative process. Here, your team are given strict time constraints and isn’t permitted to discuss ideas until the end. ‍

8. Dislodge preconceived ideas

Humans are creatures of habit.

We defer to strategies that have produced positive results in the past. This is typically beneficial because recalling our previous successes means we don’t need to constantly re-learn similar tasks.

But when it comes to problem-solving, this way of thinking can trip us up. We become fixated on a solution that worked in the past, but when this fails we’re dismayed and left wondering what to do next.

To resolve problems effectively, your employees need to escape the precincts of their imaginations. This helps to eliminate functional fixedness—the belief that an item serves only its predefined function.

Alternative Application is an icebreaker game that encourages employees to think outside the box by coming up with different uses for everyday objects. Try this at your next meeting or team-building event and watch your team tap into their creativity. ‍

9. Level the playing field

Having a diverse group of employees at your brainstorming sessions is a good idea, but there’s one problem: the extroverted members of your team will be more vocal than the introverts.

To ensure you’re gaining insight from every member of your team, you need to give your quieter employees equal opportunities to contribute by eliminating personality biases.

Read more: What icebreaker games and questions work best for introverts?

The obvious solution, then, is to “silence” the louder participants (it’s not as sinister as it sounds, promise)—all you have to do is ban your team from debating suggestions during the ideation process.

The Lightning Decision Jam methodology gives your employees equal opportunities to contribute because much of the problem-solving process is carried out in silence. ‍

10. Take a break from the problem

Have you ever noticed how the best ideas seem to come when you’re not actively working on a problem? You may have spent hours slumped over your desk hashing out a solution, only for the “eureka!” moment to come when you’re walking your dog or taking a shower.

In James Webb Young’s book, A Technique for Producing Ideas , phase three of the process is “stepping away from the problem.” Young proclaims that after putting in the hard work, the information needs to ferment in the mind before any plausible ideas come to you.

So next time you’re in a meeting with your team trying to solve a problem, don’t panic if you don’t uncover groundbreaking ideas there and then. Allow everybody to mull over what they’ve learned, then reconvene at a later date.

The Creativity Dice methodology is a quick-fire brainstorming game that allows your team to incubate ideas while concentrating on another. ‍

11. Limit feedback sessions

The way your team delivers feedback at the end of a successful brainstorming session is critical. Left unsupervised, excessive feedback can undo all of your hard work.

Therefore, it’s wise to put a cap on the amount of feedback your team can provide. One great way of doing this is by using the One Breath Feedback technique.

By limiting your employees to one breath, they’re taught to be concise with their final comments.

16 Tried and tested problem-solving methodologies

Problem-solving methodologies keep your brainstorming session on track and encourage your team to consider all angles of the issue.

Countless methods have wiggled their way into the world of business, each one with a unique strategy and end goal.

Here are 12 of our favourite problem-solving methodologies that will help you find the best-fit solution to your troubles. ‍

12. Six Thinking Hats

Six Thinking Hats is a methodical problem-solving framework that helps your group consider all possible problems, causes, solutions and repercussions by assigning a different coloured hat to each stage of the problem-solving process.

The roles of each hat are as follows:

Blue Hat (Control): This hat controls the session and dictates the order in which the hats will be worn. When wearing the Blue Hat, your group will observe possible solutions, draw conclusions and define a plan of action.
Green Hat (Idea Generation): The Green Hat signifies creativity. At this stage of the methodology, your team will focus their efforts on generating ideas, imagining solutions and considering alternatives.
Red Hat (Intuition and Feelings): It’s time for your employees to communicate their feelings. Here, your team listen to their guts and convey their emotional impulses without justification.
Yellow Hat (Benefits and Values): What are the merits of each idea that has been put forward thus far? What positive impacts could they have?
Black or Grey Hat (Caution): What are the potential risks or shortcomings of each idea? What negative impacts could result from implicating each idea?
White Hat (Information and Data): While wearing The White Hat, your team must determine what information is needed and from where it can be obtained.

For Six Thinking Hats to work effectively, ensure your team acts within the confines of each role.

While wearing The Yellow Hat, for example, your team should only discuss the positives . Any negative implications should be left for the Black or Grey hat.

Note: Feel free to alter the hat colours to align with your cultural context. ‍

13. Lightning Decision Jam (LDJ)

Lightning Decision Jam is a nine-stage problem-solving process designed to uncover a variety of perspectives while keeping the session on track.

The process starts by defining a general topic like the internal design process, interdepartmental communication, the sales funnel, etc.

Then, armed with pens and post-it notes, your team will work through the nine stages in the following order:

Write problems (7 minutes)
Present problems (4 minutes/person)
Select problems (6 minutes)
Reframe the problems (6 minutes)
Offer solutions (7 minutes)
Vote on solutions (10 minutes)
Prioritise solutions (30 seconds)
Decide what to execute (10 minutes)
Create task lists (5 minutes)

The philosophy behind LDJ is that of constraint. By limiting discussion, employees can focus on compiling ideas and coming to democratic decisions that benefit the company without being distracted or going off on a tangent. ‍

14. The 5 Why’s

Root Cause Analysis (RCA) is the process of unearthing a problem and finding the underlying cause. To help you through this process, you can use The 5 Why’s methodology.

The idea is to ask why you’re experiencing a problem, reframe the problem based on the answer, and then ask “ why?” again. If you do this five times , you should come pretty close to the root of your original challenge.

While this might not be a comprehensive end-to-end methodology, it certainly helps you to pin down your core challenges. ‍

15. World Café

If you’ve had enough of uninspiring corporate boardrooms, World Café is the solution.

This problem-solving strategy facilitates casual conversations around given topics, enabling players to speak more openly about their grievances without the pressure of a large group.

Here’s how to do it:

Create a cosy cafe-style setting (try to have at least five or six chairs per table).
As a group, decide on a core problem and mark this as the session topic.
Divide your group into smaller teams by arranging five or six players at a table.
Assign each group a question that pertains to the session topic, or decide on one question for all groups to discuss at once.
Give the groups about 20 minutes to casually talk over each question.
Repeat this with about three or four different questions, making sure to write down key insights from each group.
Share the insights with the whole group.

World Café is a useful way of uncovering hidden causes and pitfalls by having multiple simultaneous conversations about a given topic. ‍

16. Discovery and Action Dialogue (DAD)

Discovery and Actions Dialogues are a collaborative method for employees to share and adopt personal behaviours in response to a problem.

This crowdsourcing approach provides insight into how a problem affects individuals throughout your company and whether some are better equipped than others.

A DAD session is guided by a facilitator who asks seven open-ended questions in succession. Each person is given equal time to participate while a recorder takes down notes and valuable insights.

This is a particularly effective method for uncovering preexisting ideas, behaviours and solutions from the people who face problems daily. ‍

17. Design Sprint 2.0

The Design Sprint 2.0 model by Jake Knapp helps your team to focus on finding, developing measuring a solution within four days . Because theorising is all well and good, but sometimes you can learn more by getting an idea off the ground and observing how it plays out in the real world.

Here’s the basic problem-solving framework:

Day 1: Map out or sketch possible solutions
Day 2: Choose the best solutions and storyboard your strategy going forward
Day 3: Create a living, breathing prototype
Day 4: Test and record how it performs in the real world

This technique is great for testing the viability of new products or expanding and fixing the features of an existing product. ‍

18. Open Space Technology

Open Space Technology is a method for large groups to create a problem-solving agenda around a central theme. It works best when your group is comprised of subject-matter experts and experienced individuals with a sufficient stake in the problem.

Open Space Technology works like this:

Establish a core theme for your team to centralise their efforts.
Ask the participants to consider their approach and write it on a post-it note.
Everybody writes a time and place for discussion on their note and sticks it to the wall.
The group is then invited to join the sessions that most interest them.
Everybody joins and contributes to their chosen sessions
Any significant insights and outcomes are recorded and presented to the group.

This methodology grants autonomy to your team and encourages them to take ownership of the problem-solving process. ‍

19. Round-Robin Brainstorming Technique

While not an end-to-end problem-solving methodology, the Round-Robin Brainstorming Technique is an effective way of squeezing every last ounce of creativity from your ideation sessions.

Here’s how it works:

Decide on a problem that needs to be solved
Sitting in a circle, give each employee a chance to offer an idea
Have somebody write down each idea as they come up
Participants can pass if they don’t have anything to contribute
The brainstorming session ends once everybody has passed

Once you’ve compiled a long list of ideas, it’s up to you how you move forward. You could, for example, borrow techniques from other methodologies, such as the “vote on solutions” phase of the Lightning Decision Jam. ‍

20. Failure Modes and Effects Analysis (FMEA)

Failure Modes and Effects Analysis is a method for preventing and mitigating problems within your business processes.

This technique starts by examining the process in question and asking, “What could go wrong?” From here, your team starts to brainstorm a list of potential failures.

Then, going through the list one by one, ask your participants, “Why would this failure happen?”

Once you’ve answered this question for each list item, ask yourselves, “What would the consequences be of this failure?”

This proactive method focuses on prevention rather than treatment. Instead of waiting for a problem to occur and reacting, you’re actively searching for future shortcomings. ‍

21. Flip It!

The Flip It! Methodology teaches your team to view their concerns in a different light and frame them instead as catalysts for positive change.

The game works like this:

Select a topic your employees are likely to be concerned about, like market demand for your product or friction between departments.
Give each participant a pile of sticky notes and ask them to write down all their fears about the topic.
Take the fears and stick them to an area of the wall marked “fears.”
Then, encourage your team to look at these fears and ask them to reframe them as “hope” by writing new statements on different sticky notes.
Take these “hope” statements and stick them to an area of the wall marked “hope.”
Discuss the statements, then ask them to vote on the areas they feel they can start to take action on. They can do this by drawing a dot on the corner of the sticky note.
Move the notes with the most votes to a new area of the wall marked “traction.”
Discuss the most popular statements as a group and brainstorm actionable items related to each.
Write down the actions that need to be made and discuss them again as a group.

This brainstorming approach teaches your employees the danger of engrained thinking and helps them to reframe their fears as opportunities. ‍

22. The Creativity Dice

The Creativity Dice teaches your team to incubate ideas as they focus on different aspects of a problem. As we mentioned earlier in the article, giving ideas time to mature can be a highly effective problem-solving strategy. Here’s how the game works:

Choose a topic to focus on, It can be as specific or open-ended as you like. Write this down as a word or sentence. Roll the die, start a timer of three minutes and start writing down ideas within the confines of what that number resembles. The roles of each number are as follows:

Specification: Write down goals you want to achieve.
Investigation: Write down existing factual information you know about the topic.
Ideation: Write down creative or practical ideas related to the topic.
Incubation: Do something else unrelated to the problem.
Iteration: Look at what you’ve already written and come up with related ideas (roll again if you didn’t write anything yet). ‍
Integration: Look at everything you have written and try to create something cohesive from your ideas like a potential new product or actionable next step.

Once you’ve finished the activity, review your findings and decide what you want to take with you. ‍

23. SWOT Analysis

The SWOT Analysis is a long-standing method for analysing the current state of your business and considering how this affects the desired end state.

The basic idea is this:

Before the meeting, come up with a “Desired end state” and draw a picture that represents this on a flipchart or whiteboard.
Divide a large piece of paper into quadrants marked “Strengths”, “Weaknesses”, “Opportunities” and “Threats.”
Starting with “Strengths”, work through the quadrants, coming up with ideas that relate to the desired end state.
Ask your team to vote for the statements or ideas of each category that they feel are most relevant to the desired end state.
As a group, discuss the implications that these statements have on the desired end state. Spark debate by asking thought-provoking and open-ended questions.

The SWOT Analysis is an intuitive method for understanding which parts of your business could be affecting your long-term goals. ‍

24. The Journalistic Six

When learning to cover every aspect of a story, journalists are taught to ask themselves six essential questions:

Now, this approach has been adopted by organisations to help understand every angle of a problem. All you need is a clear focus question, then you can start working through the six questions with your team until you have a 360-degree view of what has, can and needs to be done. ‍

25. Gamestorming

Gamestorming is a one-stop creative-thinking framework that uses various games to help your team come up with innovative ideas.

Originally published as a book 10 years ago, Gamestorming contained a selection of creative games used by Silicon Valley’s top-performing businesses to develop groundbreaking products and services.

This collection of resources, plucked from the minds of founders and CEOs like Jeff Bezos and Steve Jobs, allows you to tap into the potentially genius ideas lying dormant in the minds of your employees. ‍

26. Four-Step Sketch

The Four-Step Sketch is a visual brainstorming that provides an alternative to traditional discussion-based ideation techniques .

This methodology requires prior discussion to clarify the purpose of the activity. Imagine you’re on a startup retreat , for example, and your team is taking part in a design sprint or hackathon.

Once you’ve brainstormed a list of ideas with your team, participants can look at the suggestions and take down any relevant notes. They then take these notes and turn them into rough sketches that resemble the idea.

Then, as a warm-up, give each participant eight minutes to produce eight alternative sketches (eight minutes per sketch) of the idea. These ideas are not to be shared with the group.

Finally, participants create new sketches based on their favourite ideas and share them with the group. The group can then vote on the ideas they think offer the best solution. ‍

27. 15% Solutions

15% Solutions is a problem-solving strategy for motivating and inspiring your employees. By encouraging your team to gain small victories, you pave the way for bigger changes.

First, ask your participants to think about things they can personally do within the confines of their role.

Then, arrange your team into small groups of three to four and give them time to share their ideas and consult with each other.

This simple problem-solving process removes negativity and powerlessness and teaches your team to take responsibility for change.

9 Problem-solving tools for gathering and selecting ideas

Problem-solving tools support your meeting with easy-to-use graphs, visualisations and techniques.

By implementing a problem-solving tool, you break the cycle of mundane verbal discussion, enabling you to maintain engagement throughout the session. ‍

28. Fishbone Diagram

The Fishbone Diagram (otherwise known as the Ishikawa Diagram or Cause and Effect Diagram), is a tool for identifying the leading causes of a problem. You can then consolidate these causes into a comprehensive “Problem Statement.”

The term “Fishbone Diagram” is derived from the diagram’s structure. The problem itself forms the tail, possible causes radiate from the sides to form the fish skeleton while the final “Problem Statement” appears as the “head” of the fish.

Example: A fast-food chain is investigating the declining quality of their food. As the team brainstorms potential causes, they come up with reasons like “poorly trained personnel”, “lack of quality control”, and “incorrect quantity of spices.” Together with other causes, the group summarises that these problems lead to “bad burgers.” They write this as the Problem Statement and set about eliminating the main contributing factors. ‍

29. The Problem Tree

A Problem Tree is a useful tool for assessing the importance or relevance of challenges concerning the core topic. If you’re launching a new product, for example, gather your team and brainstorm the current issues, roadblocks and bottlenecks that are hindering the process.

Then, work together to decide which of these are most pressing. Place the most relevant issues closer to the core topic and less relevant issues farther away. ‍

30. SQUID Diagram

The Squid Diagram is an easy-to-use tool that charts the progress of ideas and business developments as they unfold. Your SQUID Diagram can remain on a wall for your team to add to over time.

Write down a core theme on a sticky note such as “customer service” or “Innovation”—this will be the “head” of your SQUID.
Hand two sets of different coloured sticky notes to your participants and choose one colour to represent “questions” and the other to represent “answers.”
Ask your team to write down questions pertaining to the success of the main topic. In the case of “Innovation,” your team might write things like “How can we improve collaboration between key stakeholders?”
Then, using the other coloured sticky notes, ask your team to write down possible answers to these questions. In the example above, this might be “Invest in open innovation software.”
Over time, you’ll develop a spawling SQUID Diagram that reflects the creative problem-solving process. ‍

31. The Speed Boat

The Speed Boat Diagram is a visual metaphor used to help your team identify and solve problems in the way of your goals.

Here’s how it works:

Draw a picture of a boat and name it after the core objective.
With your team, brainstorm things that are slowing progress and draw each one as an anchor beneath the boat.
Discuss possible solutions to each problem on the diagram.

This is an easy-to-use tool that sparks creative solutions. If you like, your team can assign a “weight” to each anchor which determines the impact each problem has on the end goal. ‍

32. The LEGO Challenge

LEGO is an excellent creative-thinking and problem-solving tool used regularly by event facilitators to help teams overcome challenges.

In our article 5 and 10-minute Team-Building Activities , we introduce Sneak a Peek —a collaborative team-building game that develops communication and leadership skills. ‍

33. The Three W’s: What? So What? Now What?

Teams aren’t always aligned when it comes to their understanding of a problem. While the problem remains the same for everyone, they might have differing opinions as to how it occurred at the implications it had.

Asking “ What? So What? Now What?” Helps you to understand different perspectives around a problem.

It goes like this:

Alone or in small groups, ask your employees to consider and write What happened. This should take between five and 10 minutes.
Then ask So What? What occurred because of this? Why was what happened important? What might happen if this issue is left unresolved?
Finally, ask your team Now What? What might be a solution to the problem? What actions do you need to take to avoid this happening again?

This approach helps your team understand how problems affect individuals in different ways and uncovers a variety of ways to overcome them. ‍

34. Now-How-Wow Matrix

Gathering ideas is easy—but selecting the best ones? That’s a different story.

If you’ve got a bunch of ideas, try the Now-How-Wow Matrix to help you identify which ones you should implement now and which ones should wait until later.

Simply draw a two-axis graph with “implementation difficulty” on the Y axis and “idea originality” on the X axis. Divide this graph into quadrants and write “Now!” in the bottom left panel, “Wow!” in the bottom right panel, and “How?” in the top right panel. You can leave the top left panel blank.

Then, take your ideas and plot them on the graph depending on their implementation difficulty and level of originality.

By the end, you’ll have a clearer picture of which ideas to ignore, which ones to implement now, and which ones to add to the pipeline for the future. ‍

35. Impact-Effort Matrix

The Impact-Effort Matrix is a variation of the Now-How-Wow Matrix where the Y axis is marked “Impact” and the X axis is marked “Effort.”

Then, divide the graph into quadrants and plot your ideas.

Top left section = Excellent, implement immediately
Top right section = Risky, but worth a try
Bottom left section = Low risk, but potentially ineffective
Bottom right section = Bad idea, ignore

The Impact-Effort Matrix is a simple way for your team to weigh the benefits of an idea against the amount of investment required. ‍

36. Dot Voting

Once you’ve gathered a substantial list of ideas from your employees, you need to sort the good from the bad.

Dot voting is a simple tool used by problem-solving facilitators as a fast and effective way for large groups to vote on their favourite ideas . You’ll have seen this method used in problem-solving methods like Flip It! and Lightning Decision Jam .

Participants write their ideas on sticky notes and stick them to the wall or a flipchart.
When asked, participants draw a small dot on the corner of the idea they like the most.
Participants can be given as many votes as necessary.
When voting ends, arrange the notes from “most popular” to “least popular.”

This provides an easy-to-use visual representation of the best and worst ideas put forward by your team.

Give your problems the attention they deserve at an offsite retreat

While working from home or at the office, your team is often too caught up in daily tasks to take on complex problems.

By escaping the office and uniting at an offsite location, you can craft a purposeful agenda of team-building activities and problem-solving sessions. This special time away from the office can prove invaluable when it comes to keeping your business on track.

If you have problems that need fixing (who doesn’t?), reach out to Surf Office and let us put together a fully-customised offsite retreat for you.

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The problem-solving process, how to solve problems: 5 steps, train to solve problems with lean today, what is problem solving steps, techniques, & best practices explained.

Problem solving is the art of identifying problems and implementing the best possible solutions. Revisiting your problem-solving skills may be the missing piece to leveraging the performance of your business, achieving Lean success, or unlocking your professional potential.

Ask any colleague if they’re an effective problem-solver and their likely answer will be, “Of course! I solve problems every day.”

Problem solving is part of most job descriptions, sure. But not everyone can do it consistently.

Problem solving is the process of defining a problem, identifying its root cause, prioritizing and selecting potential solutions, and implementing the chosen solution.

There’s no one-size-fits-all problem-solving process. Often, it’s a unique methodology that aligns your short- and long-term objectives with the resources at your disposal. Nonetheless, many paradigms center problem solving as a pathway for achieving one’s goals faster and smarter.

One example is the Six Sigma framework , which emphasizes eliminating errors and refining the customer experience, thereby improving business outcomes. Developed originally by Motorola, the Six Sigma process identifies problems from the perspective of customer satisfaction and improving product delivery.

Lean management, a similar method, is about streamlining company processes over time so they become “leaner” while producing better outcomes.

Trendy business management lingo aside, both of these frameworks teach us that investing in your problem solving process for personal and professional arenas will bring better productivity.

1. Precisely Identify Problems

As obvious as it seems, identifying the problem is the first step in the problem-solving process. Pinpointing a problem at the beginning of the process will guide your research, collaboration, and solutions in the right direction.

At this stage, your task is to identify the scope and substance of the problem. Ask yourself a series of questions:

What’s the problem?
How many subsets of issues are underneath this problem?
What subject areas, departments of work, or functions of business can best define this problem?

Although some problems are naturally large in scope, precision is key. Write out the problems as statements in planning sheets . Should information or feedback during a later step alter the scope of your problem, revise the statements.

Framing the problem at this stage will help you stay focused if distractions come up in later stages. Furthermore, how you frame a problem will aid your search for a solution. A strategy of building Lean success, for instance, will emphasize identifying and improving upon inefficient systems.

2. Collect Information and Plan

The second step is to collect information and plan the brainstorming process. This is another foundational step to road mapping your problem-solving process. Data, after all, is useful in identifying the scope and substance of your problems.

Collecting information on the exact details of the problem, however, is done to narrow the brainstorming portion to help you evaluate the outcomes later. Don’t overwhelm yourself with unnecessary information — use the problem statements that you identified in step one as a north star in your research process.

This stage should also include some planning. Ask yourself:

What parties will ultimately decide a solution?
Whose voices and ideas should be heard in the brainstorming process?
What resources are at your disposal for implementing a solution?

Establish a plan and timeline for steps 3-5.

3. Brainstorm Solutions

Brainstorming solutions is the bread and butter of the problem-solving process. At this stage, focus on generating creative ideas. As long as the solution directly addresses the problem statements and achieves your goals, don’t immediately rule it out.

Moreover, solutions are rarely a one-step answer and are more like a roadmap with a set of actions. As you brainstorm ideas, map out these solutions visually and include any relevant factors such as costs involved, action steps, and involved parties.

With Lean success in mind, stay focused on solutions that minimize waste and improve the flow of business ecosystems.

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4. Decide and Implement

The most critical stage is selecting a solution. Easier said than done. Consider the criteria that has arisen in previous steps as you decide on a solution that meets your needs.

Once you select a course of action, implement it.

Practicing due diligence in earlier stages of the process will ensure that your chosen course of action has been evaluated from all angles. Often, efficient implementation requires us to act correctly and successfully the first time, rather than being hurried and sloppy. Further compilations will create more problems, bringing you back to step 1.

5. Evaluate

Exercise humility and evaluate your solution honestly. Did you achieve the results you hoped for? What would you do differently next time?

As some experts note, formulating feedback channels into your evaluation helps solidify future success. A framework like Lean success, for example, will use certain key performance indicators (KPIs) like quality, delivery success, reducing errors, and more. Establish metrics aligned with company goals to assess your solutions.

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Art of Problem Solving: 11 Brilliant Problem Solving Methods and Techniques Nobody Taught You

No one likes problems, especially at work. However, they’re part of our everyday work routine. If you take a look at job ads online, many of them will list “problem solvin g techniques” as a necessity for the job role. The truth is that every job in the world requires the art of problem solving.

From managing tasks to managing people, we don’t like feeling stuck, at work or outside of it. The good news is, that there are lots of tried and tested problem solving techniques that you can use to easily solve difficult situations at work or in your personal life.

11 Problem solving techniques and methods

Here are some of those problem solving methods and how you can use them in practice.

Let’s start with the basics. No matter how bad the problem or how serious the situation is, you can do one simple thing: breathe in, breathe out, and let’s begin with the art of problem solving.

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Art of problem solving

Most people get stressed out at the mere mention of a problem. They feel like they need to come up with an answer immediately; they look for someone to blame, and they want a quick and easy exit. All of a sudden, facing a problem becomes a problem of its own.

For this very reason, it’s important to slow down and take a breather. When we are stressed out, we make one critical mistake—we resort to something called binary problem-solving . In other words, we limit our options by trying out proven problem solving techniques instead of something new and more efficient.

For this reason alone, slow down and breathe; you will come up with more ways to tackle a problem.

11 Brilliant problem-solving techniques nobody taught you Click To Tweet

Ask great questions

Asking questions is part of the pre-problem-solving stage. When you ask questions, your brain can come up with different scenarios and ways to make a decision. For example, a child will usually ask questions like “What if,” “Why not,” “Can we?,” “How about?” and many others. What rules should you break? Are there any beliefs we should drop? The more questions you ask, the easier it will be to find a solution to your problem.

Don’t just trust yourself

One of the many reasons why problems come up and stay unsolved is because we are too lazy or busy to distance ourselves from them. In other words, we just think from our own perspective instead of zooming out and looking at the bigger picture , where we can utilize our problem solving techniques.

For example, if you’re in our industry (SaaS), you may have a situation where people sign up for your app and disappear after the trial period. Sure, you could try generating more traffic to your website , but there are other things you can do. Here are some questions you can ask yourself:

Has my business industry changed?
Does my app really meet my customers’ needs?
Does my sales strategy need improvement?

In another scenario, your employee shows up late for work, despite several of your warnings. Before taking any actions, try to understand their perspective and ask yourself the following questions:

Do they have any non-work-related problems in their life?
What is (literally) stopping them from getting to work?
How can I help them with problems solving?

Both situations have one thing in common – they look at the big picture before trying to tackle a specific problem.

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Do some heavy brainstorming to help the problem solving process.

A brainstorming session is one of the most effective ways to learn the art of problem solving. The gist of it is to generate as many ideas as you can and in the problem solving process, come up with a way to solve a problem. Of course, the prerequisite for any brainstorming session is a nonjudgmental, friendly environment.

If you want to brainstorm like a pro, you need to take the following steps:

HMW or How Might We

Start the session with a question such as “How might we…?” to inspire creativity among your team. The question should be open enough to inspire and foster creativity. However, it should also be focused and narrow enough to keep your session participants focused on the problem at hand.

Write down everything

Every member of your brainstorming session should write down all of their ideas, either on a board or on sticky notes. Once you have all of your ideas, put them down on a common board. If you are unable to generate sufficient ideas, repeat the session with the same question to master the art of problem solving.

Discuss your ideas

To discuss each of the ideas you and your team came up with, use phrases like “I like…”, “I wish…”, “What if…”, and others.

Select the best ideas

Now that you have all of your ideas in one place, it’s time to find the best one. For example, you could let the participants vote using sticky notes. You can also create buckets for ideas, such as “Rational choice”, “The best solution for everyone”, and others.

Using this approach, you’ll be able to save some ideas that at first seem crazy but actually make a lot of sense in the long run.

Figure out the problem-solving process

At this stage, you have your best brainstorming ideas. This is the time to choose the best ones and come up with a plan on how to bring them to life .

The Round-Robin technique for brainstorming

If traditional brainstorming just doesn’t work for you, there are other things you can try. If your team members sit and listen and hope that someone else will fix things for them, you need to try out the Round-Robin problem-solving method. In simple terms, this technique will require every participant to be actively involved in the brainstorming session. There is a lot of different brainstorming tools and apps .

There are just two rules:

– Participants take turns to contribute ideas, using the option to “pass” if they have nothing to contribute in that round.

– The brainstorming session is over once everyone makes a pass.

There is an ocean of creative problem-solving techniques for tackling any workplace issue Click To Tweet

The silent brainstorming technique

The problem with most brainstorming sessions is that the loudest people are the most likely to have their idea chosen as a solution. The quiet ones may have an excellent idea but they just sit around and never have a chance to be heard. You get the feeling that it’s more important to be active and loud than have a great idea.

If you see that happening a lot, maybe it’s time for a silent brainstorming session. You can make it happen online or in the office, the process is the same. The entire team develops ideas on their own and shares them without sitting at the same table. The main idea is that everyone’s opinion has the same weight. If you choose to do it online, it’s actually even easier to come up with a decision.

Six thinking hats

If you’re a fan of Harry Potter, you know the Sorting Hat very well. It’s a hat that students wear and it appoints them to a house in Hogwarts that best matches their personality. Along those lines, there is a technique that Edward de Bono came up with, called The six thinking hats . Using this problem solving technique, you can wear six different hats with six different perspectives.

Here are the hats that you can wear to learn the art of problem solving.

White hat. This is the neutral hat that uses facts and figures required to solve a problem. When the problem just comes up, this is the hat that you want to wear.
Red hat. This hat is all about emotion and intuition. When you wear this hat, you can show your gut reactions to ideas and freely express exactly how you feel.
Black hat. When you want to show caution and express a critical viewpoint, this is the hat you want to wear. The black hat will make sure that you steer clear of bad decisions.
Yellow hat. When you want to be positive, this hat is the one you should choose. It helps you identify the positive sides of an idea and an excellent counterweight to the black hat.
Green hat. To explore creativity, possibilities, alternatives and fresh ideas, wear a hat in green. Contributing new ideas and options is crucial, which is why everyone should wear a green hat.
Blue hat. This is the hat that organizes all others. This is the person that manages the entire decision-making process and makes sure that all other hats follow the rules and guidelines.

The six thinking hats problem-solving process is excellent because it lets you see the same problem from several different angles, very quickly and easily.

When you quickly want to get to the root of a problem, try out this technique. All you need to do is ask the question “Why” five times. Start with the problem at hand and ask why it happened, making sure that your answer is objective. Continue asking “Why” for four more times. At some point, you’ll reach the true answer to your question and you can start looking for a solution.

The biggest challenge with this technique is giving rational, objective answers to each “why”. Fight the urge to answer from your point of view. Instead, think of the logical reason why something happened. Remember, admitting that you don’t know something is far better than giving a subjective answer.

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Failure Mode and Effects Analysis (FMEA)

Want to solve problems like the big boys at Chrysler, Ford and General Motors? This advanced problem solving process lets you solve problems easily. You can use it to analyze each element of your strategy and tear it apart to see how and when it can fail. By looking into the effect of each failure and how likely it is to happen, you’ll get to the best problem solving techniques. In the end, come up with a list of actions to take to prevent each of the failures you listed in the previous steps.

The wanderer problem-solving technique

When I write articles such as this one, I have one way to make them better. Once they’re done, I let them sit for a day without taking a look at them. When I get back to the article, I take a look at it with a fresh set of eyes.

You can use the same approach with your problems. Take a step back and walk away from it. Get some rest, walk outside for a bit, watch some cat videos on YouTube. In other words, remove yourself from the situation. You just may find the answer to your problem the moment your brain relaxes.

Leave room for imagination

If nothing I listed above helps you solve a problem, this is the time to get creative. If you have a way to problem solving outside of work, it may be a good idea to apply it at work too.

For example, there is an extreme case of Yoshiro Nakamotso. The name may not sound familiar, but you probably used one of this man’s patents today. He has more than 3,300 patents to his name, including a digital wristwatch, karaoke machine, a floppy disk, and many others. He came up with a crazy problem-solving technique called The Calm Room.

His Calm Room is actually a bathroom filled with 24-karat gold. This material blocks radio waves and TV signals which according to him are harmful to solving problems. He also considers oxygen to be detrimental to problem-solving . Apparently, too much oxygen means that there will be an inspiration and this is his idea of using imagination for problem-solving.

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You can try and use the Calm Room method for solving problems or you can find other ways that let you use your imagination instead of cold, hard facts to solve an issue at work.

Develop problem solving skills

The most important point to remember is that problems happen all the time and they will keep happening. Moreover, if a problem happens at work, it will also give us information on things we need to fix. The goal of each of the problem solving processes mentioned is to make your company more open to friendly problem-solving.

To summarize, the following are the key takea ways from these problem-solving techniques.

– Keep calm and avoid high and dry approaches to problem solving

– Ask great questions, a lot of them

– Take a look at the bigger picture and the overall context of a situation

– Try out unconventional brainstorming techniques: Round-Robin and silent brainstorming

– Wear each of the Six thinking hats to take a look at different approaches to a problem solving

– Ask the 5 Whys

– Prevent any potential problems with the Failure Mode and Effects Analysis

– Leave some room for imagination at the end.

Depending on the context, you may use one or more of these problem-solving processes – make sure to choose one that works best for your situation, team and personality. Good luck!

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This is a very good article. I find it useful for my adult learners.

Hi Antonette. We try our best to be useful for our readers. Glad you enjoyed reading this post.

I find this to be very resourceful both personal use and grooming future managers as they develop their skills.

Thanks for this great work.

Hey Daniel! Nice to hear your feedback, we’ll do our best to keep on writing good post.

The article is no doubt useful . I observed that many people at the higher management level are afraid to accept the true cause of the problem as they fear of action against them. As management strategy there has to be a rule that any body accepting truth should not be punished on the contrary he must be empowered to solve the problem at his level only. Many problems can be solved the moment you accept the truth. I have solved many problems by using this theory during my 32 years of service in the engineering management field.

This article was very , Very , very much helpful for my college assignment. I’d say thanks trillion times to you 🙂

Hello Pruthviraj, that’s so great to hear! Thank you.

This is a very depth and resourceful article.

Very useful topic which countians very important tips for solving problems.

Thanks and keep up the good work.

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Problem solving techniques: Steps and methods

Posted on May 29, 2019

Constant disruption has become a hallmark of the modern workforce and organisations want problem solving skills to combat this. Employers need people who can respond to change – be that evolving technology, new competitors, different models for doing business, or any of the other transformations that have taken place in recent years.

In addition, problem solving techniques encompass many of the other top skills employers seek . For example, LinkedIn’s list of the most in-demand soft skills of 2019 includes creativity, collaboration and adaptability, all of which fall under the problem-solving umbrella.

Despite its importance, many employees misunderstand what the problem solving method really involves.

What constitutes effective problem solving?

Effective problem solving doesn’t mean going away and coming up with an answer immediately. In fact, this isn’t good problem solving at all, because you’ll be running with the first solution that comes into your mind, which often isn’t the best.

Instead, you should look at problem solving more as a process with several steps involved that will help you reach the best outcome. Those steps are:

Define the problem
List all the possible solutions
Evaluate the options
Select the best solution
Create an implementation plan
Communicate your solution

Let’s look at each step in a little more detail.

It's important you take the time to brainstorm and consider all your options when solving problems.

1. Define the problem

The first step to solving a problem is defining what the problem actually is – sounds simple, right? Well no. An effective problem solver will take the thoughts of everyone involved into account, but different people might have different ideas on what the root cause of the issue really is. It’s up to you to actively listen to everyone without bringing any of your own preconceived notions to the conversation. Learning to differentiate facts from opinion is an essential part of this process.

An effective problem solver will take the opinions of everyone involved into account

The same can be said of data. Depending on what the problem is, there will be varying amounts of information available that will help you work out what’s gone wrong. There should be at least some data involved in any problem, and it’s up to you to gather as much as possible and analyse it objectively.

2. List all the possible solutions

Once you’ve identified what the real issue is, it’s time to think of solutions. Brainstorming as many solutions as possible will help you arrive at the best answer because you’ll be considering all potential options and scenarios. You should take everyone’s thoughts into account when you’re brainstorming these ideas, as well as all the insights you’ve gleaned from your data analysis. It also helps to seek input from others at this stage, as they may come up with solutions you haven’t thought of.

Depending on the type of problem, it can be useful to think of both short-term and long-term solutions, as some of your options may take a while to implement.

One of the best problem solving techniques is brainstorming a number of different solutions and involving affected parties in this process.

3. Evaluate the options

Each option will have pros and cons, and it’s important you list all of these, as well as how each solution could impact key stakeholders. Once you’ve narrowed down your options to three or four, it’s often a good idea to go to other employees for feedback just in case you’ve missed something. You should also work out how each option ties in with the broader goals of the business.

There may be a way to merge two options together in order to satisfy more people.

4. Select an option

Only now should you choose which solution you’re going to go with. What you decide should be whatever solves the problem most effectively while also taking the interests of everyone involved into account. There may be a way to merge two options together in order to satisfy more people.

5. Create an implementation plan

At this point you might be thinking it’s time to sit back and relax – problem solved, right? There are actually two more steps involved if you want your problem solving method to be truly effective. The first is to create an implementation plan. After all, if you don’t carry out your solution effectively, you’re not really solving the problem at all.

Create an implementation plan on how you will put your solution into practice. One problem solving technique that many use here is to introduce a testing and feedback phase just to make sure the option you’ve selected really is the most viable. You’ll also want to include any changes to your solution that may occur in your implementation plan, as well as how you’ll monitor compliance and success.

6. Communicate your solution

There’s one last step to consider as part of the problem solving methodology, and that’s communicating your solution . Without this crucial part of the process, how is anyone going to know what you’ve decided? Make sure you communicate your decision to all the people who might be impacted by it. Not everyone is going to be 100 per cent happy with it, so when you communicate you must give them context. Explain exactly why you’ve made that decision and how the pros mean it’s better than any of the other options you came up with.

Prove your problem solving skills with Deakin

Employers are increasingly seeking soft skills, but unfortunately, while you can show that you’ve got a degree in a subject, it’s much harder to prove you’ve got proficiency in things like problem solving skills. But this is changing thanks to Deakin’s micro-credentials. These are university-level micro-credentials that provide an authoritative and third-party assessment of your capabilities in a range of areas, including problem solving. Reach out today for more information .

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The Eight Fundamentals of Problem Solving

As business leaders we are consequently required to solve problems. But what are the very fundamentals of problem solving?

Read on to find out.

1. Define the Real Problem

This is the biggie. Ensure that you are solving the right problem. Toyota is justifiably famous for its problem-solving savvy in perfecting its production methods. According to Toyota, the key to their method is to spend relatively more time defining the problem and relatively less time on figuring out the solution.

2. Solve the Root Cause of the Problem

Don’t treat the symptoms; solve the root cause of the problem. There are numerous methods to determine root causes—cause mapping, fishbone diagrams, etc. For me, the easiest and most effective is to use the “Five Whys.” Ask a question and to each answer ask. “Why?” again. Doing this for five times should get you to the root cause of the problem.

3. Use a Hypothesis

As happens on the “CSI” television shows, you should make a best guess as to the solution to the problem at the very beginning of your process—define the initial hypothesis. Then test this initial hypothesis by digging deep to determine whether the hypothesis is right or wrong and adjusting the hypothesis as the facts dictate.

4. Get the Facts

Dig deep and get the facts to truly understand the nature of the problem and the possible solutions. Do the analysis to let the facts do the talking instead of gut instinct. As Wharton’s own Peter Cappelli says: “I tell my MBA students that whenever you are going with your gut, you are doing something wrong. In most cases, you can actually figure it out. So you should sit down and figure it out.”

5. Keep the solution simple

Any solution to a problem has to be implemented by your team. So keep it simple. Be able to explain the solution clearly and precisely in 30 seconds. Limit the action items to solve the problem to three. Go for the solution that solves 80 percent of the problem but that is 100 percent implementable by the team—rather than a 100 percent solution that is unlikely to ever be properly implemented.

6. Do not re-invent the wheel

Plagiarism can be good. If someone has a clever idea or way to solve your problem, by all means legally use it. The “not invented here” syndrome is just sheer arrogance.

7. Gain momentum in problem solving

In situations where you have multiple problems to solve (e.g., business turnarounds) pluck the low-hanging but important fruit first. Solve the easy problems. This gives you momentum, shows progress and gives your team confidence.

8. Consider time

With any solution, ensure that you do first what needs to be done first. Also, ensure that the solution can be implemented in a reasonable period of time. Solutions that take longer than a few months will likely fail. The momentum will die out or top management will move on to another “critical issue.”

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A Better Framework for Solving Tough Problems

Start with trust and end with speed.

Apple Podcasts

When it comes to solving complicated problems, the default for many organizational leaders is to take their time to work through the issues at hand. Unfortunately, that often leads to patchwork solutions or problems not truly getting resolved.

But Anne Morriss offers a different framework. In this episode, she outlines a five-step process for solving any problem and explains why starting with trust and ending with speed is so important for effective change leadership. As she says, “Let’s get into dialogue with the people who are also impacted by the problem before we start running down the path of solving it.”

Morriss is an entrepreneur and leadership coach. She’s also the coauthor of the book, Move Fast and Fix Things: The Trusted Leader’s Guide to Solving Hard Problems .

Key episode topics include: strategy, decision making and problem solving, strategy execution, managing people, collaboration and teams, trustworthiness, organizational culture, change leadership, problem solving, leadership.

HBR On Strategy curates the best case studies and conversations with the world’s top business and management experts, to help you unlock new ways of doing business. New episodes every week.

Listen to the full HBR IdeaCast episode: How to Solve Tough Problems Better and Faster (2023)
Find more episodes of HBR IdeaCast
Discover 100 years of Harvard Business Review articles, case studies, podcasts, and more at HBR.org .

HANNAH BATES: Welcome to HBR On Strategy , case studies and conversations with the world’s top business and management experts, hand-selected to help you unlock new ways of doing business.

When it comes to solving complicated problems, many leaders only focus on the most apparent issues. Unfortunately that often leads to patchwork or partial solutions. But Anne Morriss offers a different framework that aims to truly tackle big problems by first leaning into trust and then focusing on speed.

Morriss is an entrepreneur and leadership coach. She’s also the co-author of the book, Move Fast and Fix Things: The Trusted Leader’s Guide to Solving Hard Problems . In this episode, she outlines a five-step process for solving any problem. Some, she says, can be solved in a week, while others take much longer. She also explains why starting with trust and ending with speed is so important for effective change leadership.

This episode originally aired on HBR IdeaCast in October 2023. Here it is.

CURT NICKISCH: Welcome to the HBR IdeaCast from Harvard Business Review. I’m Curt Nickisch.

Problems can be intimidating. Sure, some problems are fun to dig into. You roll up your sleeves, you just take care of them; but others, well, they’re complicated. Sometimes it’s hard to wrap your brain around a problem, much less fix it.

And that’s especially true for leaders in organizations where problems are often layered and complex. They sometimes demand technical, financial, or interpersonal knowledge to fix. And whether it’s avoidance on the leaders’ part or just the perception that a problem is systemic or even intractable, problems find a way to endure, to keep going, to keep being a problem that everyone tries to work around or just puts up with.

But today’s guest says that just compounds it and makes the problem harder to fix. Instead, she says, speed and momentum are key to overcoming a problem.

Anne Morriss is an entrepreneur, leadership coach and founder of the Leadership Consortium and with Harvard Business School Professor Francis Frei, she wrote the new book, Move Fast and Fix Things: The Trusted Leaders Guide to Solving Hard Problems . Anne, welcome back to the show.

ANNE MORRISS: Curt, thank you so much for having me.

CURT NICKISCH: So, to generate momentum at an organization, you say that you really need speed and trust. We’ll get into those essential ingredients some more, but why are those two essential?

ANNE MORRISS: Yeah. Well, the essential pattern that we observed was that the most effective change leaders out there were building trust and speed, and it didn’t seem to be a well-known observation. We all know the phrase, “Move fast and break things,” but the people who were really getting it right were moving fast and fixing things, and that was really our jumping off point. So when we dug into the pattern, what we observed was they were building trust first and then speed. This foundation of trust was what allowed them to fix more things and break fewer.

CURT NICKISCH: Trust sounds like a slow thing, right? If you talk about building trust, that is something that takes interactions, it takes communication, it takes experiences. Does that run counter to the speed idea?

ANNE MORRISS: Yeah. Well, this issue of trust is something we’ve been looking at for over a decade. One of the headlines in our research is it’s actually something we’re building and rebuilding and breaking all the time. And so instead of being this precious, almost farbege egg, it’s this thing that is constantly in motion and this thing that we can really impact when we’re deliberate about our choices and have some self-awareness around where it’s breaking down and how it’s breaking down.

CURT NICKISCH: You said break trust in there, which is intriguing, right? That you may have to break trust to build trust. Can you explain that a little?

ANNE MORRISS: Yeah, well, I’ll clarify. It’s not that you have to break it in order to build it. It’s just that we all do it some of the time. Most of us are trusted most of the time. Most of your listeners I imagine are trusted most of the time, but all of us have a pattern where we break trust or where we don’t build as much as could be possible.

CURT NICKISCH: I want to talk about speed, this other essential ingredient that’s so intriguing, right? Because you think about solving hard problems as something that just takes a lot of time and thinking and coordination and planning and designing. Explain what you mean by it? And also, just how we maybe approach problems wrong by taking them on too slowly?

ANNE MORRISS: Well, Curt, no one has ever said to us, “I wish I had taken longer and done less.” We hear the opposite all the time, by the way. So what we really set out to do was to create a playbook that anyone can use to take less time to do more of the things that are going to make your teams and organizations stronger.

And the way we set up the book is okay, it’s really a five step process. Speed is the last step. It’s the payoff for the hard work you’re going to do to figure out your problem, build or rebuild trust, expand the team in thoughtful and strategic ways, and then tell a real and compelling story about the change you’re leading.

Only then do you get to go fast, but that’s an essential part of the process, and we find that either people under emphasize it or speed has gotten a bad name in this world of moving fast and breaking things. And part of our mission for sure was to rehabilitate speed’s reputation because it is an essential part of the change leader’s equation. It can be the difference between good intentions and getting anything done at all.

CURT NICKISCH: You know, the fact that nobody ever tells you, “I wish we had done less and taken more time.” I think we all feel that, right? Sometimes we do something and then realize, “Oh, that wasn’t that hard and why did it take me so long to do it? And I wish I’d done this a long time ago.” Is it ever possible to solve a problem too quickly?

ANNE MORRISS: Absolutely. And we see that all the time too. What we push people to do in those scenarios is really take a look at the underlying issue because in most cases, the solution is not to take your foot off the accelerator per se and slow down. The solution is to get into the underlying problem. So if it’s burnout or a strategic disconnect between what you’re building and the marketplace you’re serving, what we find is the anxiety that people attach to speed or the frustration people attach to speed is often misplaced.

CURT NICKISCH: What is a good timeline to think about solving a problem then? Because if we by default take too long or else jump ahead and we don’t fix it right, what’s a good target time to have in your mind for how long solving a problem should take?

ANNE MORRISS: Yeah. Well, we’re playful in the book and talking about the idea that many problems can be solved in a week. We set the book up five chapters. They’re titled Monday, Tuesday, Wednesday, Thursday, Friday, and we’re definitely having fun with that. And yet, if you count the hours in a week, there are a lot of them. Many of our problems, if you were to spend a focused 40 hours of effort on a problem, you’re going to get pretty far.

But our main message is, listen, of course it’s going to depend on the nature of the problem, and you’re going to take weeks and maybe even some cases months to get to the other side. What we don’t want you to do is take years, which tends to be our default timeline for solving hard problems.

CURT NICKISCH: So you say to start with identifying the problem that’s holding you back, seems kind of obvious. But where do companies go right and wrong with this first step of just identifying the problem that’s holding you back?

ANNE MORRISS: And our goal is that all of these are going to feel obvious in retrospect. The problem is we skip over a lot of these steps and this is why we wanted to underline them. So this one is really rooted in our observation and I think the pattern of our species that we tend to be overconfident in the quality of our thoughts, particularly when it comes to diagnosing problems.

And so we want to invite you to start in a very humble and curious place, which tends not to be our default mode when we’re showing up for work. We convince ourselves that we’re being paid for our judgment. That’s exactly what gets reinforced everywhere. And so we tend to counterintuitively, given what we just talked about, we tend to move too quickly through the diagnostic phase.

CURT NICKISCH: “I know what to do, that’s why you hired me.”

ANNE MORRISS: Exactly. “I know what to do. That’s why you hired me. I’ve seen this before. I have a plan. Follow me.” We get rewarded for the expression of confidence and clarity. And so what we’re inviting people to do here is actually pause and really lean into what are the root causes of the problem you’re seeing? What are some alternative explanations? Let’s get into dialogue with the people who are also impacted by the problem before we start running down the path of solving it.

CURT NICKISCH: So what do you recommend for this step, for getting to the root of the problem? What are questions you should ask? What’s the right thought process? What do you do on Monday of the week?

ANNE MORRISS: In our experience of doing this work, people tend to undervalue the power of conversation, particularly with other people in the organization. So we will often advocate putting together a team of problem solvers, make it a temporary team, really pull in people who have a particular perspective on the problem and create the space, make it as psychologically safe as you can for people to really, as Chris Argyris so beautifully articulated, discuss the undiscussable.

And so the conditions for that are going to look different in every organization depending on the problem, but if you can get a space where smart people who have direct experience of a problem are in a room and talking honestly with each other, you can make an extraordinary amount of progress, certainly in a day.

CURT NICKISCH: Yeah, that gets back to the trust piece.

ANNE MORRISS: Definitely.

CURT NICKISCH: How do you like to start that meeting, or how do you like to talk about it? I’m just curious what somebody on that team might hear in that meeting, just to get the sense that it’s psychologically safe, you can discuss the undiscussable and you’re also focusing on the identification part. What’s key to communicate there?

ANNE MORRISS: Yeah. Well, we sometimes encourage people to do a little bit of data gathering before those conversations. So the power of a quick anonymous survey around whatever problem you’re solving, but also be really thoughtful about the questions you’re going to ask in the moment. So a little bit of preparation can go a long way and a little bit of thoughtfulness about the power dynamic. So who’s going to walk in there with license to speak and who’s going to hold back? So being thoughtful about the agenda, about the questions you’re asking about the room, about the facilitation, and then courage is a very infectious emotion.

So if you can early on create the conditions for people to show up bravely in that conversation, then the chance that you’re going to get good information and that you’re going to walk out of that room with new insight in the problem that you didn’t have when you walked in is extraordinarily high.

CURT NICKISCH: Now, in those discussions, you may have people who have different perspectives on what the problem really is. They also bear different costs of addressing the problem or solving it. You talked about the power dynamic, but there’s also an unfairness dynamic of who’s going to actually have to do the work to take care of it, and I wonder how you create a culture in that meeting where it’s the most productive?

ANNE MORRISS: For sure, the burden of work is not going to be equitably distributed around the room. But I would say, Curt, the dynamic that we see most often is that people are deeply relieved that hard problems are being addressed. So it really can create, and more often than not in our experience, it does create this beautiful flywheel of action, creativity, optimism. Often when problems haven’t been addressed, there is a fair amount of anxiety in the organization, frustration, stagnation. And so credible movement towards action and progress is often the best antidote. So even if the plan isn’t super clear yet, if it’s credible, given who’s in the room and their decision rights and mandate, if there’s real momentum coming out of that to make progress, then that tends to be deeply energizing to people.

CURT NICKISCH: I wonder if there’s an organization that you’ve worked with that you could talk about how this rolled out and how this took shape?

ANNE MORRISS: When we started working with Uber, that was wrestling with some very public issues of culture and trust with a range of stakeholders internally, the organization, also external, that work really started with a campaign of listening and really trying to understand where trust was breaking down from the perspective of these stakeholders?

So whether it was female employees or regulators or riders who had safety concerns getting into the car with a stranger. This work, it starts with an honest internal dialogue, but often the problem has threads that go external. And so bringing that same commitment to curiosity and humility and dialogue to anyone who’s impacted by the problem is the fastest way to surface what’s really going on.

CURT NICKISCH: There’s a step in this process that you lay out and that’s communicating powerfully as a leader. So we’ve heard about listening and trust building, but now you’re talking about powerful communication. How do you do this and why is it maybe this step in the process rather than the first thing you do or the last thing you do?

ANNE MORRISS: So in our process, again, it’s the days of the week. On Monday you figured out the problem. Tuesday you really got into the sandbox in figuring out what a good enough plan is for building trust. Wednesday, step three, you made it better. You created an even better plan, bringing in new perspectives. Thursday, this fourth step is the day we’re saying you got to go get buy-in. You got to bring other people along. And again, this is a step where we see people often underinvest in the power and payoff of really executing it well.

CURT NICKISCH: How does that go wrong?

ANNE MORRISS: Yeah, people don’t know the why. Human behavior and the change in human behavior really depends on a strong why. It’s not just a selfish, “What’s in it for me?” Although that’s helpful, but where are we going? I may be invested in a status quo and I need to understand, okay, if you’re going to ask me to change, if you’re going to invite me into this uncomfortable place of doing things differently, why am I here? Help me understand it and articulate the way forward and language that not only I can understand, but also that’s going to be motivating to me.

CURT NICKISCH: And who on my team was part of this process and all that kind of stuff?

ANNE MORRISS: Oh, yeah. I may have some really important questions that may be in the way of my buy-in and commitment to this plan. So certainly creating a space where those questions can be addressed is essential. But what we found is that there is an architecture of a great change story, and it starts with honoring the past, honoring the starting place. Sometimes we’re so excited about the change and animated about the change that what has happened before or what is even happening in the present tense is low on our list of priorities.

Or we want to label it bad, because that’s the way we’ve thought about the change, but really pausing and honoring what came before you and all the reasonable decisions that led up to it, I think can be really helpful to getting people emotionally where you want them to be willing to be guided by you. Going back to Uber, when Dara Khosrowshahi came in.

CURT NICKISCH: This is the new CEO.

ANNE MORRISS: The new CEO.

CURT NICKISCH: Replaced Travis Kalanick, the founder and first CEO, yeah.

ANNE MORRISS: Yeah, and had his first all-hands meeting. One of his key messages, and this is a quote, was that he was going to retain the edge that had made Uber, “A force of nature.” And in that meeting, the crowd went wild because this is also a company that had been beaten up publicly for months and months and months, and it was a really powerful choice. And his predecessor, Travis was in the room, and he also honored Travis’ incredible work and investment in bringing the company to the place where it was.

And I would use words like grace to also describe those choices, but there’s also an incredible strategic value to naming the starting place for everybody in the room because in most cases, most people in that room played a role in getting to that starting place, and you’re acknowledging that.

CURT NICKISCH: You can call it grace. Somebody else might call it diplomatic or strategic. But yeah, I guess like it or not, it’s helpful to call out and honor the complexity of the way things have been done and also the change that’s happening.

ANNE MORRISS: Yeah, and the value. Sometimes honoring the past is also owning what didn’t work or what wasn’t working for stakeholders or segments of the employee team, and we see that around culture change. Sometimes you’ve got to acknowledge that it was not an equitable environment, but whatever the worker, everyone in that room is bringing that pass with them. So again, making it discussable and using it as the jumping off place is where we advise people to start.

Then you’ve earned the right to talk about the change mandate, which we suggest using clear and compelling language about the why. “This is what happened, this is where we are, this is the good and the bad of it, and here’s the case for change.”

And then the last part, which is to describe a rigorous and optimistic way forward. It’s a simple past, present, future arc, which will be familiar to human beings. We love stories as human beings. It’s among the most powerful currency we have to make sense of the world.

CURT NICKISCH: Yeah. Chronological is a pretty powerful order.

ANNE MORRISS: Right. But again, the change leaders we see really get it right, are investing an incredible amount of time into the storytelling part of their job. Ursula Burns, the Head of Xerox is famous for the months and years she spent on the road just telling the story of Xerox’s change, its pivot into services to everyone who would listen, and that was a huge part of her success.

CURT NICKISCH: So Friday or your fifth step, you end with empowering teams and removing roadblocks. That seems obvious, but it’s critical. Can you dig into that a little bit?

ANNE MORRISS: Yeah. Friday is the fun day. Friday’s the release of energy into the system. Again, you’ve now earned the right to go fast. You have a plan, you’re pretty confident it’s going to work. You’ve told the story of change the organization, and now you get to sprint. So this is about really executing with urgency, and it’s about a lot of the tactics of speed is where we focus in the book. So the tactics of empowerment, making tough strategic trade-offs so that your priorities are clear and clearly communicated, creating mechanisms to fast-track progress. At Etsy, CEO Josh Silverman, he labeled these projects ambulances. It’s an unfortunate metaphor, but it’s super memorable. These are the products that get to speed out in front of the other ones because the stakes are high and the clock is sticking.

CURT NICKISCH: You pull over and let it go by.

ANNE MORRISS: Yeah, exactly. And so we have to agree as an organization on how to do something like that. And so we see lots of great examples both in young organizations and big complex biotech companies with lots of regulatory guardrails have still found ways to do this gracefully.

And I think we end with this idea of conflict debt, which is a term we really love. Leanne Davey, who’s a team scholar and researcher, and anyone in a tech company will recognize the idea of tech debt, which is this weight the organization drags around until they resolve it. Conflict debt is a beautiful metaphor because it is this weight that we drag around and slows us down until we decide to clean it up and fix it. The organizations that are really getting speed right have figured out either formally or informally, how to create an environment where conflict and disagreements can be gracefully resolved.

CURT NICKISCH: Well, let’s talk about this speed more, right? Because I think this is one of those places that maybe people go wrong or take too long, and then you lose the awareness of the problem, you lose that urgency. And then that also just makes it less effective, right? It’s not just about getting the problem solved as quickly as possible. It’s also just speed in some ways helps solve the problem.

ANNE MORRISS: Oh, yeah. It really is the difference between imagining the change you want to lead and really being able to bring it to life. Speed is the thing that unlocks your ability to lead change. It needs a foundation, and that’s what Monday through Thursday is all about, steps one through four, but the finish line is executing with urgency, and it’s that urgency that releases the system’s energy, that communicates your priorities, that creates the conditions for your team to make progress.

CURT NICKISCH: Moving fast is something that entrepreneurs and tech companies certainly understand, but there’s also this awareness that with big companies, the bigger the organization, the harder it is to turn the aircraft carrier around, right? Is speed relative when you get at those levels, or do you think this is something that any company should be able to apply equally?

ANNE MORRISS: We think this applies to any company. The culture really lives at the level of team. So we believe you can make a tremendous amount of progress even within your circle of control as a team leader. I want to bring some humility to this and careful of words like universal, but we do think there’s some universal truths here around the value of speed, and then some of the byproducts like keeping fantastic people. Your best people want to solve problems, they want to execute, they want to make progress and speed, and the ability to do that is going to be a variable in their own equation of whether they stay or they go somewhere else where they can have an impact.

CURT NICKISCH: Right. They want to accomplish something before they go or before they retire or finish something out. And if you’re able to just bring more things on the horizon and have it not feel like it’s going to be another two years to do something meaningful.

ANNE MORRISS: People – I mean, they want to make stuff happen and they want to be around the energy and the vitality of making things happen, which again, is also a super infectious phenomenon. One of the most important jobs of a leader, we believe, is to set the metabolic pace of their teams and organizations. And so what we really dig into on Friday is, well, what does that look like to speed something up? What are the tactics of that?

CURT NICKISCH: I wonder if that universal truth, that a body in motion stays in motion applies to organizations, right? If an organization in motion stays in motion, there is something to that.

ANNE MORRISS: Absolutely.

CURT NICKISCH: Do you have a favorite client story to share, just where you saw speed just become a bit of a flywheel or just a positive reinforcement loop for more positive change at the organization?

ANNE MORRISS: Yeah. We work with a fair number of organizations that are on fire. We do a fair amount of firefighting, but we also less dramatically do a lot of fire prevention. So we’re brought into organizations that are working well and want to get better, looking out on the horizon. That work is super gratifying, and there is always a component of, well, how do we speed this up?

What I love about that work is there’s often already a high foundation of trust, and so it’s, well, how do we maintain that foundation but move this flywheel, as you said, even faster? And it’s really energizing because often there’s a lot of pent-up energy that… There’s a lot of loyalty to the organization, but often it’s also frustration and pent-up energy. And so when that gets released, when good people get the opportunity to sprint for the first time in a little while, it’s incredibly energizing, not just for us, but for the whole organization.

CURT NICKISCH: Anne, this is great. I think finding a way to solve problems better but also faster is going to be really helpful. So thanks for coming on the show to talk about it.

ANNE MORRISS: Oh, Curt, it was such a pleasure. This is my favorite conversation. I’m delighted to have it anytime.

HANNAH BATES: That was entrepreneur, leadership coach, and author Anne Morriss – in conversation with Curt Nickisch on HBR IdeaCast.

We’ll be back next Wednesday with another hand-picked conversation about business strategy from Harvard Business Review. If you found this episode helpful, share it with your friends and colleagues, and follow our show on Apple Podcasts, Spotify, or wherever you get your podcasts. While you’re there, be sure to leave us a review.

When you’re ready for more podcasts, articles, case studies, books, and videos with the world’s top business and management experts, you’ll find it all at HBR.org.

This episode was produced by Mary Dooe, Anne Saini, and me, Hannah Bates. Ian Fox is our editor. Special thanks to Rob Eckhardt, Maureen Hoch, Erica Truxler, Ramsey Khabbaz, Nicole Smith, Anne Bartholomew, and you – our listener. See you next week.

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Marines say no more ‘death by PowerPoint’ as Corps overhauls education

WASHINGTON, D.C. ― Marines and those who teach them will see more direct, problem-solving approaches to how they learn and far less “death by PowerPoint” as the Corps overhauls its education methods .

Decades of lecturers “foot stomping” material for Marines to learn, recall and regurgitate on a test before forgetting most of what they heard is being replaced by “outcomes-based” learning, a method that’s been in use in other fields but only recently brought into military training.

“Instead of teaching them what to think, we’re teaching them how to think,” said Col. Karl Arbogast, director of the policy and standards division at training and education command .

Here’s what’s in the Corps’ new training and education plan

New ranges, tougher swimming. inside the corps' new training blueprint..

Arbogast laid out some of the new methods that the command is using at the center for learning and faculty development while speaking at the Modern Day Marine Expo.

“No more death by PowerPoint,” Arbogast said. “No more ‘sage on the stage’ anymore, it’s the ‘guide on the side.’”

To do that, Lt. Col. Chris Devries, director of the learning and faculty center, is a multiyear process in which the Marines have developed two new military occupational specialties, 0951 and 0952.

The exceptional MOS is in addition to their primary MOS but allows the Marines to quickly identify who among their ranks is qualified to teach using the new methods.

Training for those jobs gives instructors, now called facilitators, an entry-level understanding of how to teach in an outcomes-based learning model.

Devries said the long-term goal is to create two more levels of instructor/facilitator that a Marine could return to in their career, a journeyman level and a master level. Those curricula are still under development.

The new method helps facilitators first learn the technology they’ll need to share material with and guide students. It also teaches them more formal assessment tools so they can gauge how well students are performing.

For the students, they can learn at their own pace. If they grasp the material the group is covering, they’re encouraged to advance in their study, rather than wait for the entire group to master the introductory material.

More responsibility is placed on the students. For example, in a land navigation class, a facilitator might share materials for students to review before class on their own and then immediately jump into working with maps, compasses and protractors on land navigation projects in the next class period, said John deForest, learning and development officer at the center.

That creates more time in the field for those Marines to practice the skills in a realistic setting.

Marines with Marine Medium Tiltrotor Squadron (VMM) 268, Marine Aircraft Group 24, 1st Marine Aircraft Wing, fire M240-B machine guns at the Marine Corps Air Station Kaneohe Bay range, Hawaii, March 5. (Lance Cpl. Tania Guerrero/Marine Corps)

For the infantry Marine course, the school split up the large classroom into squad-sized groups led by a sergeant or staff sergeant, allowing for more individual focus and participation among the students, Arbogast said.

“They have to now prepare activities for the learner to be directly involved in their own learning and then they have to steer and guide the learners correct outcome,” said Timothy Heck, director of the center’s West Coast detachment.

The students are creating products and portfolios of activities in their training instead of simply taking a written test, said Justina Kirkland, a facilitator at the West Coast detachment.

Students are also pushed to discuss problems among themselves and troubleshoot scenarios. The role of the facilitator then is to monitor the conversation and ask probing questions to redirect the group if they get off course, Heck said.

That involves more decision games, decision forcing cases and even wargaming, deForest said.

We “put the student in an active learning experience where they have to grapple with uncertainty, where they have to grapple with the technical skills and the knowledge they need,” deForest said.

That makes the learning more about application than recall, he said.

Todd South has written about crime, courts, government and the military for multiple publications since 2004 and was named a 2014 Pulitzer finalist for a co-written project on witness intimidation. Todd is a Marine veteran of the Iraq War.

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How to Solve Coding Problems: Step-by-Step Guide (2024)

May 20, 2024 · 13 min read

Coding challenges are a common obstacle for many programmers, whether they are just starting or have years of experience.

In this complete guide, we will provide expert tips and strategies for effectively solving coding problems.

By following these valuable tips, you can confidently enhance your problem-solving skills and conquer even the most challenging coding tasks.

Let's get started.

Read the Problem Statement Carefully

Identify key constraints

One imperative step in solving coding problems is identifying the key constraints in the problem statement. These constraints define the boundaries within which your solution must operate and can greatly influence your approach.

Note important variables

Carefully note down important variables mentioned in the problem statement as they often hold crucial information for solving the problem efficiently.

Understanding the significance of these variables can guide you toward the right solution approach.

Remember to consider any implicit variables that might affect your solution but are not explicitly mentioned in the problem statement.

Attention to all variables will ensure a more comprehensive understanding of the problem.

Tip: Here, you can learn about key programming definitions and terms

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Break Down Complexity

Divide into smaller Tasks

You'll find that breaking down a complex coding problem into smaller tasks makes it more manageable.

Start by identifying the different components of the problem and breaking them down into smaller subproblems. This approach will help you tackle each subproblem individually and eventually solve the larger problem.

Focus on one task

The key to successfully breaking down a complex coding problem is to focus on one task at a time.

Concentrating all your efforts on solving one specific subproblem can help you avoid feeling overwhelmed by the complexity of the overall task.

This focused approach will improve your problem-solving skills and allow you to make steady progress toward the final solution.

When focusing on one task, setting clear goals and objectives for that specific subproblem is vital. It will help you stay on track and prevent distractions derailing your problem-solving process.

By dedicating your full attention and energy to each task, you can efficiently work through the complexities of the coding problem and find an effective solution.

Tip: The Feynman learning technique is the best solution for learning how to break down complex concepts.

Research and Learn

Study similar problems

Research shows that one of the best strategies to solve coding problems easily is to study similar problems.

By analyzing how others have approached and solved comparable issues, you can gain valuable insights and techniques to apply to your challenges.

Learn new concepts

Learning new concepts is imperative for continuous improvement in coding.

By staying updated with the latest technologies, algorithms, and best practices, you can enhance your problem-solving skills and broaden your understanding of different coding techniques.

Any aspiring coder should regularly explore new concepts through online courses, tutorials, and coding challenges.

This proactive approach helps solve current problems more effectively and prepares you for future challenges in the ever-evolving tech industry.

Tip: The fastest way to learn any new concept is to share what you learn. For example, you can learn a piece of code and then use code sharing tools to share your knowledge with the audience.

Write Pseudocode First

Plan out Algorithm Steps

For effective problem-solving, it is crucial to plan out the steps of your algorithm before writing actual code.

Pseudocode helps break down the problem into smaller, manageable steps, making it easier to implement the solution in the chosen programming language.

Visualize solution flow

While writing pseudocode, visualize how the solution will flow from one step to another.

This visualization helps in understanding the logic of the algorithm and can highlight any potential issues or optimizations that can be made before writing actual code.

For instance, if you are working on a sorting algorithm, visualizing the flow can help you determine the most efficient way to arrange the elements and identify any redundant steps that you can eliminate to improve performance.

Start with Simple

Implement basic solution

Unlike complex problems, coding problems are best tackled with a straightforward approach.

Begin by implementing a basic solution that may not be the most efficient but solves the problem correctly.

This helps in understanding the problem better and getting a working solution.

Refine as needed

Implementing a basic solution is just the beginning.

As you progress, refine your code by optimizing it for performance, readability, and scalability.

Refactoring code to improve efficiency and incorporating best practices will boost your solution to the next level.

A key strategy for refining your code is to analyze its complexity and identify areas for optimization. This may involve revisiting your algorithm choices and data structures or breaking down the problem into smaller, manageable parts.

By continuously refining your solution, you improve your coding skills and enhance the quality of your code.

Use Online Resources

Leverage coding communities

Despite the various challenges of coding problems, the process becomes easier when you tap into the wealth of knowledge available in coding communities.

These online platforms, such as Stack Overflow and GitHub, offer a supportive environment where you can seek solutions, ask questions, and learn from experienced programmers.

Consult online tutorials

These resources provide step-by-step guidance on various programming concepts and problem-solving techniques, making grasping complex algorithms and data structures easier.

The abundance of online tutorials ranges from beginner to advanced, and they are fit for programmers of all proficiency levels.

By consulting these tutorials, you can enhance your understanding of coding principles and develop effective strategies for solving various coding problems.

Any aspiring coder should take advantage of the vast array of online resources that can facilitate the process of solving coding problems.

By leveraging coding communities, consulting online tutorials, and exploring other online platforms, you can quickly sharpen your problem-solving skills and become a more proficient programmer.

Tip: Resources like YouTube and Udemy are great ways. But you can also read the best development books to enhance your coding skills further.

Debug Thoroughly

Identify common mistakes

Unlike overlooking small errors, identifying common mistakes is crucial in debugging code efficiently.

Any coder should be aware of recurring issues like:

Syntax Errors
Logical mistakes
Incorrect variable usage

By recognizing these patterns, programmers can initiate debugging and write cleaner code.

Test edge cases

Any comprehensive debugging strategy should include testing edge cases to ensure code reliability and robustness.

By intentionally pushing the boundaries of input values or conditions, developers can uncover potential mistakes that might go unnoticed during regular testing.

This practice helps programmers anticipate and address unexpected scenarios, leading to more resilient code.

Testing edge cases involves evaluating the extremes of input data or conditions to verify the code's behavior under challenging circumstances.

By examining how the program handles unusual or extreme values, developers can identify vulnerabilities or inefficiencies that may occur in real-world usage.

Practice Regularly

Build problem-solving muscle

Your coding skills are like a muscle that needs regular exercise to strengthen. Make a habit of solving coding problems daily to enhance your problem-solving abilities.

Develop coding instincts

Build a strong intuition for coding by practicing regularly.

As you solve more problems, you'll notice patterns and common strategies that can help you tackle new problems more efficiently.

Developing coding instincts involves understanding different approaches to problem-solving and knowing when to apply them. This initiative will guide you in choosing the most effective solutions and optimizing your code for better performance.

Review and Refine

Analyze solution efficiency

Unlike simply finding a solution, it is imperative to analyze its efficiency.

Evaluate the time complexity, space complexity, and overall performance of the code.

This step will help you understand how the code will perform with larger inputs and whether there are any bottlenecks that need to be addressed.

Optimize code quality

Coding problems are not just about finding a solution but also about writing clean and efficient code.

Pay attention to coding standards, readability, and best practices.

Refactor the code to make it more concise, understandable, and maintainable. This step is crucial in ensuring that your code is not only functional but also of high quality.

You can use tools like linters and code formatters to check and improve your code's quality automatically.

These tools can help you catch potential errors, enforce coding standards, and enhance the overall readability of your codebase.

By optimizing your code quality, you can make it easier for yourself and others to understand and work with the code in the future.

Tip: You can use a code review checklist to optimize code efficiency quickly.

Learn from Others

Study open-source code

Study open-source code to truly enhance your coding skills.

By studying the work of experienced developers, you can gain insight into different perspectives, problem-solving techniques, and coding styles.

This exposure can broaden your knowledge and inspire innovative solutions to coding problems.

Learn from mentors

Some of the most effective learning experiences come from mentors who can provide guidance, feedback, and real-world insights.

Connecting with experienced professionals in the field can offer valuable advice, help you navigate challenges, and accelerate your learning process.

Learn from mentors who have expertise in your specific area of interest.

Their guidance can help you grasp complex concepts, avoid common pitfalls, and stay updated on industry trends.

Building a strong mentorship relationship can significantly impact your coding journey and foster professional growth.

Stay Calm and Patient

Manage problem-solving stress

After encountering a challenging coding problem, managing the stress that comes with it is imperative.

Take deep breaths, step back, and remind yourself that feeling stuck is okay.

Keeping a clear mind will help you approach the problem more effectively.

Take breaks when needed

If you find yourself hitting a wall and getting frustrated, it's time to take a break.

Stepping away from the problem for a few minutes or even an hour can improve your mental clarity.

Some fresh air or a quick walk can help reset your mind and improve focus when you return to the task.

When stress builds up, it can blur your thinking and make problem-solving even more challenging.

Taking breaks gives you a chance to relax and allows your brain to subconsciously work on the problem in the background, often leading to new insights and solutions.

Identify Patterns

Recognize common patterns

One vital skill in solving coding problems is recognizing common patterns.

By identifying recurring themes or structures in the problem you're trying to solve, you can apply similar solutions that have worked in the past. It can help simplify your problem-solving process and lead to more efficient coding.

Apply pattern-based solutions

To effectively apply pattern-based solutions, you need to understand different types of patterns commonly found in coding problems.

These patterns can include algorithms like sliding windows, two-pointers, or depth-first search.

By leveraging these patterns, you can quickly develop solutions that have been proven to work for similar problems.

Tip: You can explore different development frameworks to identify common patterns.

Draw Diagrams

Visualize problem structure

When faced with a complex coding problem, start by visualizing its structure.

Use diagrams to represent different components, their relationships, and data flow. This visual representation can clarify the problem and help you identify key areas to focus on.

Illustrate solution flow

While solving coding problems, illustrating the solution flow through diagrams can facilitate the problem-solving process.

Create a step-by-step flowchart or sequence diagram to map the logic and algorithm.

This visual aid can guide you through the implementation phase and help you identify potential errors or optimizations in the solution.

Diagrams can also serve as documentation for your code, making it easier for others to understand your thought process and approach.

By incorporating visual elements into your problem-solving strategies, you can enhance your efficiency and accuracy in coding.

Collaborate with Peers

Work with coding partners

For an effective problem-solving strategy, consider working with coding partners.

Collaborating with peers can help you bounce ideas off each other, share different approaches, and collectively develop innovative solutions.

By leveraging your peers diverse skills and perspectives, you can tackle coding problems more efficiently and effectively.

Learn from peer feedback

Even the most experienced coders can benefit from constructive feedback from their peers.

Peer feedback can provide valuable insights into alternative solutions, code optimization techniques, and potential pitfalls to avoid.

You can continuously improve your problem-solving skills and expand your coding knowledge by actively seeking and incorporating feedback from your coding peers.

Work with your coding partners to brainstorm ideas, discuss different approaches, and troubleshoot any challenges you encounter.

Creating a collaborative environment with your peers can enhance your problem-solving abilities and accelerate your learning process.

Final Words

Mastering the key skills mentioned above will help you solve coding problems more easily and efficiently.

Buffing your problem-solving skills, staying organized, and utilizing various techniques such as pseudocoding and debugging can help you tackle coding challenges with confidence and precision.

Keep practicing and implementing these strategies to enhance your problem-solving abilities and become a more skilled coder.

Why is code optimization important in the problem-solving process?

Code optimization is important in the problem-solving process because it improves the code's performance and efficiency. Optimized code runs faster, requires less memory, and performs better with large input sizes. Optimization reduces the code's time and space complexity and ensures that it meets performance requirements.

Why is testing your code with different test cases important in coding problem-solving?

Testing your code with different test cases helps ensure your solution works correctly for various scenarios. It also helps identify edge cases, errors, and potential bugs in the code. Thorough testing enhances the reliability and accuracy of your code.

Original Article
Open access
Published: 27 May 2024
Volume 98 , article number 47 , ( 2024 )

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Jorge Ventura 1 ,
Fernando Martinez 1 ,
Francisco Manzano-Agugliaro ORCID: orcid.org/0000-0002-0085-030X 1 ,
Aleš Návrat 2 ,
Jaroslav Hrdina 2 ,
Ahmad H. Eid 3 &
Francisco G. Montoya 1

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This paper introduces a novel method for solving the resection problem in two and three dimensions based on conformal geometric algebra (CGA). Advantage is taken because of the characteristics of CGA, which enables the representation of points, lines, planes, and volumes in a unified mathematical framework and offers a more intuitive and geometric understanding of the problem, in contrast to existing purely algebraic methods. Several numerical examples are presented to demonstrate the efficacy of the proposed method and to compare its validity with established techniques in the field. Numerical simulations indicate that our vector geometric algebra implementation is faster than the best-known algorithms to date, suggesting that the proposed GA-based methods can provide a more efficient and comprehensible solution to the two- and three-dimensional resection problem, paving the way for further applications and advances in geodesy research. Furthermore, the method’s emphasis on graphical and geometric representation makes it particularly suitable for educational purposes, allowing the reader to grasp the concepts and principles of resection more effectively. The proposed method has potential applications in a wide range of other fields, including surveying, robotics, computer vision, or navigation.

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1 Introduction

The resection problem, also known in surveying as the Snellius–Pothenot (SP) or the inverse intersection problem, involves calculating the position of an unknown point P (also called a station) using the positions of three known points A , B , and C , and relative angular measurements from P . It is a relevant problem not only in geodesy and surveying, but also in other disciplines such as robot path planning (Masselli and Zell 2014 ), positioning (Pierlot and Van Droogenbroeck 2014 ), navigation (Pereira et al. 2018 ) or computer graphics (Mazaheri and Habib 2015 ), and can be solved both geometrically and algebraically. The solution of the two-dimensional problem has been known for several centuries and has numerous variants [almost 500! according to Bock ( 1956 )]. The three-dimensional problem is much more intricate and only complex and sophisticated algebraic solutions are known. The two- and three-dimensional configurations are illustrated in Fig. 1 .

Representation of the resection problem in 2D (left) and 3D (right)

1.1 Motivation

The determination of the position of an observer based on angular measurements from known points is of interest in several disciplines, such as surveying, computer graphics, optics, and robotics. Traditionally, solutions to this problem have relied on heavily algebraically loaded methods, which can be complex and challenging to comprehend. Furthermore, these methods do not always provide an intuitive understanding of the geometric relationships involved in the problem.

In both two-dimensional (2D) and three-dimensional (3D) problems, there is a need for a more geometric or graphical approach that simplifies the study of the resection problem. Although there are existing graphical methods for solving the problem in 2D that have been known for some time, their algebraic implementation can be quite cumbersome, hindering their widespread adoption. When the problem is approached from a geometric perspective, a better understanding of the underlying structures and relationships can be achieved, making the problem more accessible to a wider range of researchers and practitioners. This could potentially lead to novel applications and advancements in the related areas mentioned above.

In light of the exposed ideas, the main motivation behind this paper is to develop a novel geometric method based on conformal geometric algebra (CGA) to address the resection problem in two- and three-dimensional ways. By leveraging the unifying properties of CGA to represent geometric primitives within a single mathematical framework, we aim to provide a more intuitive and geometric understanding of the problem, simplifying its study, and paving the way for further applications and advancements in the field.

1.2 Background and literature overview

The resection problem has been extensively studied in the literature, with various algebraic and geometric or graphical methods proposed for its solution. It appears that ancient Greeks, such as Hipparchus or Ptolemy, already studied this problem in the context of astronomy, although the first person to solve the problem in the context of surveying was the Dutch mathematician Willebrord Snel van Royen (known as Snellius) in 1617 (Wreede 2007 ). He achieved the goal by using geometric and algebraic methods mainly based on trigonometry. This same problem was addressed in 1671 by John Collins in his work Philosophical Transactions . Collins contributed significantly to the topic by presenting a new and elegant geometrical solution, which involves the use of just one circle and an auxiliary point. In 1692, Laurent Pothenot, who was working on the definition of the meridian north of Paris, presented a paper on the subject. However, according to McCaw ( 1918 ) and others, Pothenot did not contribute anything new to the solution of the problem and all he did was publish the works of Snellius and Collins under his own name. Other authors who have studied this issue are shown in Table 1 .

In the context of geodesy and surveying, the resection problem has been a fundamental problem for centuries. The problem has been addressed from various perspectives, including algebraic (Awange et al. 2010 ), geometric/graphical (Masselli and Zell 2014 ), and numerical (Dekov 2012 ) methods. Algebraic solutions to the problem are well established and have been extensively studied. However, these methods often involve complex algebraic manipulations and do not provide any intuitive geometric understanding of the problem.

The two-dimensional problem has been solved using approaches such as graphical methods (Bock 1956 ), analytical geometry (Bil 1992 ), matrix methods (Bähr 1991 ), and algebraic methods based on Sylvester resultants (Awange and Grafarend 2002 ), Groebner bases (Awange 2002 ), and other elimination techniques (Sturmfels 2002 ). Awange and Grafarend ( 2005 ) provided a detailed overview of several algebraic techniques for solving 2D and 3D resection.

The three-dimensional version is more complex, with most solutions relying on intricate algebraic methods. Grunert originally formulated the problem in 1841 and derived quartic equations to determine the unknown distances (Grunert 1841 ). Since then, numerous procedures have been developed to optimise Grunert’s formulation and reduce the computational steps involved (Awange and Grafarend 2005 ; Fischler and Bolles 1981 ). Algebraic techniques such as Groebner bases (Awange and Grafarend 2003a ), polynomial resultants (Awange and Grafarend 2003b ), and linear homotopy (Paláncz et al. 2010 ) have been effectively applied to solve the 3D problem. However, geometric solutions to the resection problem have been less explored. The geometric or graphical approach provides a more intuitive understanding of the problem and can be more easily visualised.

In recent years, there has been a growing interest in the application of geometric algebra (GA) to solve several geometric problems. GA provides a unified mathematical framework for representing and manipulating geometric objects, making it a powerful tool for geometric computations (Dorst et al. 2010 ). The application of GA to the resection problem was first proposed by Smith ( 2023b , 2023a ).

However, the application of GA to the resection problem is still in its early stages, and there is still a long way to go. In particular, the application of conformal geometric algebra (CGA) to the resection problem has not been fully explored. CGA extends GA by incorporating the concept of conformal transformations, which can provide a more powerful and flexible framework for geometric computations (Hestenes and Sobczyk 2012 ; Dorst et al. 2010 ). CGA provides a unified framework for handling points, lines, planes, circles, spheres, and other geometric entities. Each entity has a unique representation, and the relationships between entities correspond to algebraic relationships between their CGA representations. This eliminates the need for coordinate transformations when transitioning between reference frames.

Cameron and Lasenby ( 2008 ) showed that CGA subsumes projective geometry and is more computationally efficient than matrix methods. CGA has found applications in computer vision (Wareham et al. 2004 ), robotics (Zaplana et al. 2022 ), and other geometric computing problems (Hitzer et al. 2022 ). However, its potential for solving resection-type problems in geodesy and surveying remains relatively unexplored. This paper seeks to fill the void by introducing a new geometric solution based on CGA for the 2D and 3D resection problem.

1.3 Contributions

In this paper, a new method for solving the resection problem using the mathematical framework geometric algebra in 2D and 3D dimensions is proposed. The method provides a simple solution based on purely geometric and graphical principles. Specifically, the 3D version of the problem is thoroughly analysed in detail. Specific novel contributions are the following:

A novel conformal geometric algebra (CGA)-based method is presented to solve the two- and three-dimensional resection problem, providing a more intuitive and unified geometric approach.

The proposed method is compared with established techniques, and its advantages and efficacy are demonstrated through numerical examples.

The potential applications of the method in several fields such as computer graphics, optics, and robotics are highlighted, emphasising its versatility, and paving the way for future advancements in geometric research.

Several algorithms have been developed that provide better results than the best-known algorithms to date from a computational perspective.

1.4 Outline

The remainder of the article is organised as follows. Section 2 provides an introduction to geometric algebra and conformal geometric algebra. Section 3 revisits the resection problem and reviews traditional methods. Section 4 presents existing and new GA-based methods. Section 4 presents the proposed method based on CGA to solve the resection problem. Section 5 provides several application examples to demonstrate the effectiveness of the proposed method, along with benchmarks for computational efficiency. Section 6 provides an error and uncertainty analysis of the proposed methods. Finally, Sect. 7 concludes the article with a summary and some suggestions for future work.

2 Basics concepts in geometric algebra

Geometric algebra is a mathematical framework for representing geometric objects and transformations in a unified way (Hestenes and Sobczyk 2012 ). GA extends the algebra of vectors to include other geometric objects such as points, lines, planes, and volumes. GA provides a powerful tool to solve geometric problems and has applications in a wide range of fields, including electrical engineering (Montoya et al. 2019 , 2021 ), computer vision (Hrdina and Návrat 2017 ), robotics (Hrdina et al. 2017 ), and other engineering fields [see Hitzer et al. ( 2022 ) and references there in].

GAs are used mainly in situations where Euclidean transformations play a significant role. A simple way to introduce GAs is to understand them through more familiar tools such as complex numbers or quaternions (indeed, they are subalgebras of GA). For example, implementing Euclidean rotations using quaternions is essential to improve computational capabilities and adopt an object-oriented approach. We can see quaternions ${\mathbb {H}}$ as a natural extension of the complex numbers ${\mathbb {C}}$ in the form

where $a,b,c,d \in \mathbb R$ and the products of the basis elements $\varvec{i},\varvec{j},\varvec{k}$ satisfy the multiplications rules $\varvec{i}^2=\varvec{j}^2=\varvec{k}^2=-1$ and $\varvec{ij}=-\varvec{ji}=\varvec{k}$ . The quaternion $\text {Im} (\varvec{z})=b \varvec{i} + c \varvec{j} +d\varvec{k}$ is called the imaginary part of $\varvec{z}$ , and $\text {Re} (\varvec{z})=a$ is called the real part of $\varvec{z}$ . Note the use of bold letters for quaternions and regular font for real numbers.

The operation of rotating an object by an angle $\theta $ around the axis $\varvec{n}= n_x \varvec{i}+ n_y \varvec{j}+ n_z \varvec{k} $ can be represented by the quaternion

acting on the vector $\varvec{q}= x\varvec{i} +y\varvec{j} +z\varvec{k}$ . Note that $||\varvec{n}||=\sqrt{\varvec{n}\bar{\varvec{n}}}=1$ , where the bar decoration stands for quaternionic conjugation. The representation is done in a similar way as in the case of complex numbers. The difference is that quaternions are not commutative and thus they act via the so-called sandwich product

So, we are working in a four-dimensional linear space. If we want to realise also the translations, we have to extend the algebra by another dimension using an element $\varvec{\epsilon }$ such as $\varvec{\epsilon }^2=0$ and $\varvec{\epsilon } \varvec{i}=\varvec{\epsilon } \varvec{j}=\varvec{\epsilon } \varvec{k}=0$ . This algebra is usually called dual quaternions. For more on the use of quaternions in general engineering topics, see Selig ( 2005 ).

On the other hand, the wedge operation on a vector space allows us to work with linear subspaces. A line can be characterised by a vector $\varvec{\ell }$ , so x belongs to a line if and only if $x \wedge \varvec{\ell }=0$ . The wedge of two vectors then characterises the plane in the same way. A vector space closed in the wedge operation is called a Grassmannian algebra. The combination of these two concepts leads to the notion of GA.

2.1 Euclidean vector GA

Vector geometric algebra (VGA) is perhaps one of the simplest GAs. For the two-dimensional case, the VGA ( $\mathbb G_2$ ) is a Grassmannian algebra based on two orthonormal basis vectors ( $\varvec{\sigma }_1$ , $\varvec{\sigma }_2$ ) together with a bilinear operation known as geometric product satisfying the following identities:

The term $\varvec{\sigma }_1 \wedge \varvec{\sigma }_2$ is known as bivector ( $\varvec{\sigma }_{12}$ for short). Geometrically, a bivector represents an oriented plane segment spanned by the two vectors. We can use bivectors to represent rotations in the following way. The collection of bivectors $\varvec{\sigma }_1 \wedge \varvec{\sigma }_2$ forms a one-dimensional vector space that is closed under multiplication. We can then generate rotations by applying the exponential map to bivectors. For example, the exponential of the bivector

is used as in ( 3 ) to perform a rotation by an angle $\theta $ in the plane spanned by $\varvec{\sigma }_1$ and $\varvec{\sigma }_2$ . In this way, the group of rotations generated by the bivectors is mathematically equivalent to the group of unitary complex numbers $e^{i\theta }$ , which also represent rotations in the complex plane (note that $(\varvec{\sigma }_1 \wedge \varvec{\sigma }_2 )^2 =-1$ ). However, bivectors provide a more intuitive geometric representation of rotations directly in vector space.

Similarly, we can introduce the $\mathbb G_3$ algebra for the purposes of reasoning in the 3D space. The algebra $\mathbb G_3$ is based on three generators $\varvec{\sigma }_1, \varvec{\sigma }_2$ and $\varvec{\sigma }_3$ together with a geometric product defined by the following identities:

In Sect. 4.1 , it will be shown how to use the VGA-based method to solve a 2D version of the resection problem. This procedure is, in fact, a use of GA $\mathbb G_2$ .

2.2 Conformal geometric algebra

The goal here is to create a model of Euclidean geometry. Specifically, geometry whose symmetry group contains the Euclidean symmetries (rotations, translations, etc.). For that purpose, a nondegenerate quadratic form will be chosen, thus obtaining the conformal geometric algebra (CGA). In the case of CGA for a two-dimensional Euclidean space, a GA of signature (3, 1) is obtained [also known as Compass Rule Algebra CRA, see Hildenbrand ( 2018 )], with basis vectors $\varvec{\sigma }_1,\varvec{\sigma }_2,\varvec{\sigma }_+$ and $\varvec{\sigma }_-$ such that

For mathematical convenience, it is advisable to define two new basis vectors

with properties

Vector $\varvec{\sigma }_0$ is known to represent the Euclidean point at the origin of the coordinate system, and vector $\varvec{\sigma }_{\infty }$ represents the point at infinity. Using the rules above, it can be proved that any Euclidean point X can be mapped to the CGA vector space as

In “Appendix A.1”, explicit calculations that justify our choices can be found. As in Sect. 2.1 , the extension to higher dimensions is straightforward by adding the element $\varvec{\sigma }_3$ . This will make $\mathbb G_3$ appear instead of $\mathbb G_2$ , and quaternions will appear in the bivectors.

In the notation used throughout this paper to ensure clarity, regular font indicates real numbers, boldface denotes vectors in the CGA space, boldface with an overhead arrow (e.g. $\vec {\varvec{x}}$ ) represents vectors in the Euclidean space, and uppercase letters in boldface indicate multivectors in CGA.

The usefulness of CGA and CRA is based on the fact that the distance between Euclidean points is encoded in the scalar product. The points X and Y are represented by the Euclidean vectors $\vec {\varvec{x}}$ and $\vec {\varvec{y}}$ , respectively. The mapping defined in ( 12 ) maps these Euclidean points (vectors) to vector elements $\varvec{{x}}$ and $\varvec{{y}}$ in the CGA space.

As shown in “Appendix A.2”, the scalar product between two CGA points codes the distance:

Thus, the Euclidean point X (represented by the Euclidean vector $\vec {\varvec{x}}$ ) lies on the sphere (circle) S with centre in point C and radius r if and only if it satisfies the identity $\varvec{{x}} \cdot \varvec{{c}} = -\frac{1}{2} r^2 $ in the conformal space. Since $\varvec{x}\cdot \varvec{\sigma }_{\infty }=-1$ for each point, this identity may be written as

Thus, the vector element $\varvec{{c}} - \frac{1}{2} r^2 \varvec{\sigma }_{\infty } $ represents the sphere S in the CGA space. It should be emphasised that within CGA, there exist two distinctive methods to reference the identical geometric entity: IPNS and OPNS (see “Appendix A.3”). IPNS is superior for transformations and intersections, whereas OPNS is advantageous for blending and morphing tasks. It is crucial to be aware of the representation we are operating in; however, transitioning between representations can be achieved seamlessly using the dual operator ( $^\star $ ), as described in “Appendix A.3”.

3 Revisiting the resection problem

In the context of geodesy and surveying, the resection problem plays an important role in determining the position of an observer based on angular measurements from three known reference points. Over the years, various approaches have been developed to address this problem, ranging from graphical or geometrical methods to algebraic ones. However, many of these methods can be complex or tedious, particularly when addressing the problem in three dimensions. With the growing importance of accurate positioning in modern applications, it is essential to revisit the resection problem and explore innovative approaches that offer more intuitive solutions.

3.1 Traditional methods

In this section, traditional methods for solving the resection problem are reviewed. They can be classified into four basic groups: trigonometric, geometric/graphical, iterative (numerical) and others (see Table 2 ). A comprehensive list of methods for 2D resection problems is already presented in Table 1 . Note that sometimes the frontier between trigonometric and geometric methods is not as clear because both solutions exist at the same time (e.g. the Cassini method).

Trigonometric methods are some of the oldest and most famous procedures for solving the 2D resection problem. They are based on the use of trigonometric functions to compute the position of the observer using the angles between the known points and the observer.

The Pothenot–Snellius method, also known as the Kästner–Burkhardt method, is one of the most known and oldest procedures in this group. The Cassini method is another example of a trigonometric solution (with a graphical solution, too), which is similar to the one described by Esteves et al. and Cohen and Koss. The Easton and Cameron method is also a trigonometric approach, similar to the Cassini method.

Geometric or graphical methods, on the other hand, use geometrical constructions and properties of the known points to calculate the position of the observer. These methods are based on the use of geometric and graphic principles to solve the problem. Esteves et al. proposed a geometric method that uses the intersection of circles to calculate the position of the observer. Cohen and Koss also proposed a geometric method that uses the intersection of circles, but with a different approach from Esteves et al. Font-Llagunes proposed a method that uses the intersection of lines and similarity between triangles to calculate the position of the observer. Pierlot et al. and Ligas proposed a method that uses the intersection of power lines to calculate the position of the observer, although the solution is given in algebraic form.

Iterative methods use iterative algorithms to converge to the observer position. These methods are based on the use of an initial estimate of the observer position, which is refined iteratively until convergence is achieved. Iterative search is an example of an iterative method that uses a search algorithm to find the robot position. Sanchiz et al. proposed a method that uses an iterative search algorithm to find the observer position.

Finally, there are other methods that do not fit the previous groups. The Tienstra method is one such example, which is a completely different approach based on barycentric coordinates. Another method like Willerding is based on the use of complex numbers to compute rotations in the Argand plane to find the observer position.

4 Resection using geometric algebra

Nowadays, methods based on geometric algebra (GA) have been developed, providing a new solution to the resection problem while maintaining the focus on its geometrical roots. GA offers a versatile framework that can be adapted to different contexts based on the selection of specific metrics and the number of dimensions. For example, when all elements of the base $\varvec{\sigma }_i$ square to $+1$ , the resulting algebra is known as vector geometric algebra (VGA) (see Sect. 2.1 ). By extending the ability of the basis elements to square to $-1$ or 0 or by accommodating more dimensions, it becomes possible to explore alternative forms of GA. One such example is CGA, which incorporates two additional dimensions: one dimension squaring to $+1$ and another squaring to $-1$ . This flexibility enables GA to solve a wide array of applications and problem domains, seamlessly scaling the number of dimensions in a straightforward way.

4.1 Vector GA method

The 2D VGA-based method has been recently proposed by Smith ( 2023a ) and published as disseminative material. The process is mainly geometric and results in obtaining a vector $\varvec{p}$ that describes the position of the point P when choosing the middle point ( B ) as the origin. In this case, we start with a vector basis consisting of two elements $\varvec{\sigma } =\{\varvec{\sigma }_1, \varvec{\sigma }_2\}$ . Figure 2 illustrates a representation of the problem, as well as a detailed sequence of steps carried out.

Vector GA-based method steps to solve the 2D resection problem

First, using the known data ( A , B , C , $\alpha $ , and $\beta $ ), circles $c_1$ and $c_2$ are drawn using points A , B , P and B , C , P , respectively (see Fig. 2 a). These circles serve as an auxiliary element for better understanding the solution, but are not required as such. With the help of the central angle theorem, the vectors $\varvec{d}_1$ and $\varvec{d}_2$ are obtained

where $\varvec{v}_1=A-B$ and $\varvec{v}_2=C-B$ . Note that B was chosen as the origin, but any other point can also be selected under the condition that $\alpha $ or $\beta $ is not null. This situation occurs when P is collinear with two of the three known points. In such a case, other points can be selected as the origin. Equation ( 15 ) indicates that vectors $\varvec{d}_i$ are the result of rotating and scaling vectors $\varvec{v}_i$ , as shown in Fig. 2 b. Note that the rotation angle is given by $(90-\alpha )$ and $(90-\beta )$ , respectively. The next step involves determining the vector $\varvec{d}$ as $\varvec{d}_2-\varvec{d}_1$ . Finally, the desired vector $\varvec{p}$ is the rejection of $\varvec{d}_1$ or $\varvec{d}_2$ on $\varvec{d}$ (see Fig. 2 c). In VGA, the above steps are summarised in the following equation

It should be noted that the proposed solution is remarkably simple and does not involve the use of any type of coordinates. The result is obtained by simple geometric operations, such as rotation, scaling, and rejection, applied to the inherent primitives of VGA, such as vectors in this specific case.

The proposed method has advantages over the existing ones. It avoids some limitations as in Tienstra’s method where no solution can be found if the points A , B , and C are collinear. Furthermore, it is feasible to obtain an indicator of how close P is to the forbidden circle (defined by points A , B , and C ) by means of the length of vector $\varvec{d}$ . If the point P is on this circle, then it can be easily checked that $d=\Vert \varvec{d}\Vert = 0$ . Consequently, small values of d suggest that we should relocate the station to another site to ensure a reduced source of error (see Sect. 6 for a detailed error analysis).

4.2 Conformal GA method

The methodology employing VGA, as outlined in Sect. 4.1 , primarily utilised the GA $\mathbb {G}_2$ . However, given that the resection problem primarily deals with circles, utilising its conformal extension, specifically the compass ruler algebra (CRA), appears to be more suitable (see Hildenbrand 2018 ). When dealing with geometric problems, it is highly advantageous to have a tool that can express graphical methods algebraically.

On the basis of the postulates presented in Sect. 2.2 , two traditional and well-known graphical methods are proposed to solve the resection problem using CRA: Cassini and Collins. By leveraging CRA, both methods can receive clear algebraic interpretations, as explained in the following sections.

For a more in-depth example of CRA using the Clifford library in Python, see the GitHub repository.

4.2.1 Cassini construction

The Cassini method provides a solution to the resection problem by leveraging the inscribed angle theorem. The solution is obtained by determining the intersection of two circles: one passing through points A , B , and P , and the other through points B , C , and P as shown in Fig. 3 . To determine the centres of the circles, two lines must be intersected. The step-by-step graphical approach underlying the Cassini method can be elucidated, along with the equivalent steps, using the CRA algebra (see Fig. 4 ).

2D graphical resection procedure using Cassini method

Graphical solution of Cassini method step by step. The point P is found by intersecting the two circles $c_1$ and $c_2$ where all the points see AB with angle $\alpha $ and BC with angle $\beta $ , respectively

CRA version of Cassini’s method step by step

CRA Mapping : The problem starts by mapping three known Euclidean points, A , B , and C , to the CRA domain. For example, the point A with coordinates $(a_1,a_2)$ is mapped as

For the rotated lines $\varvec{\ell }_{AO_{1}}$ and $\varvec{\ell }_{CO_{2}}$ , the following rotors and translators must be first defined

, and thus,

Note that rotations are always relative to the origin. To rotate around an arbitrary point, it must first be translated to the origin. The rotation is then applied, followed by another translation that returns the point back to its original position.

Circle building : The centres of the circles can now be found as the intersection of the lines $\varvec{\ell }_{AB}$ and $\varvec{\ell }_{AO_{1}}$ and $\varvec{\ell }_{BC}$ and $\varvec{\ell }_{CO_{2}}$

The result is a flat point, representing the wedge of the sought point and the point at infinity. Footnote 1 The extraction of the point of interest is straightforward by factoring out the point at infinity

The radius of the circles can be computed as

, and the circles themselves are determined as

Intersection of circles : The desired result can be obtained from the intersection of the two circles $\varvec{c}_1$ and $\varvec{c}_2$ as

Two intersecting circles in CGA yield a couple of points (1D sphere), also known as pair-point $\varvec{P}$ . Finally, the Euclidean point P is recovered by the classic formula (see Hildenbrand 2018 )

One of the points $ P_{\pm }$ is exactly the point B , and the other is the sought point P (see Fig. 3 ).

Figure 5 shows a concise and condensed summary of the key steps involved and discussed above. It provides valuable visual depictions that enhance the geometric intuition underlying the method, offering an algebraic interpretation of the graphical approach. It also helps to reinforce the strong connection between the graphical Cassini method and its algebraic translation using CRA.

The GitHub repository shows several examples derived from the code developed by the authors. The computational procedures in CGA are found to be straightforward. The methodology involves the manipulation and combination of geometric objects, thus justifying the occasional reference to GA as an object-oriented approach.

Collin’s method for solving the resection problem

4.2.2 Collins construction

The graphical method of Collins provides a solution to the resection problem using the intersection of the line passing through the point B and the so-called Collins auxiliary point E with the circle containing the points A , C , and E . The step-by-step procedure for applying Collins’ method graphically is depicted in Fig. 6 .

CRA version of Collins’ Method step by step

CRA Mapping : Similarly to the Cassini method, the points A , B , and C must be mapped to CGA as

Auxiliary Point : To determine the auxiliary point E , it is necessary to define the lines $\ell _{AE}$ and $\ell _{CE}$ as shown in Fig. 6 b by first rotating the line through A and C $(\ell _{AC})$ an angle $\beta $ around the point A in a counterclockwise direction

and then rotate the line $\ell _{AC}$ around C by an angle $\alpha $ clockwise

The intersection of the two lines determines the position of the Collins auxiliary point E

We get the Collins point as a flat point and use the standard projection to receive E .

Circle and Line intersection : Using the points A , C , and E , the circle c that passes through them is built

The end point P we are looking for is found by intersecting the circle c and the line through E and B (see Fig. 6 d),

The intersection of a line and a circle results in a pair-point $\varvec{P}$ . As in the previous method, Eq. ( 26 ) is used to extract the two distinct points, one of them being the point E and the other the sought point P .

Figure 7 shows a visual summary of the key steps of the Collins method.

Step-by-step construction of the graphical solution for the resection problem in 3D

4.3 Resection method in 3D

The construction procedure for the 3D case is carried out in a series of detailed steps, as in the 2D sections and as illustrated in Fig. 8 . The main idea is to project all points into a plane parallel to the reference plane $\varvec{\sigma }_{12}$ (the plane xy ). It can be any, but we chose the one that passes through one of the known points (for example, point A ). Then, we apply one of the methods presented in the previous sections to this simplified 2D version of the original problem, and finally, we solve for the $\varvec{\sigma }_3$ ( z ) coordinate of the projected point. Section 5 provides specific examples.

CRA Mapping : Represent Euclidean points $A,B,C \in \mathbb R^3$ in VGA as vectors $\vec {\varvec{x}}=x_1 \varvec{\sigma }_1 +x_2 \varvec{\sigma }_2 + x_3 \varvec{\sigma }_3$ , project them into the xy plane ( $\varvec{\sigma }_1 \wedge \varvec{\sigma }_2 = \varvec{\sigma }_{12}$ ) by formulas

Note that, for computational purposes, it is sufficient to remove component $x_3$ for this specific case. The points are now mapped to the CRA domain

2D Solution : Use one of the methods described in Sect. 4.2 to solve the problem restricted to the plane xy , obtaining the points $P_1$ and $P_2$ . The choice point will be designated as $P_p$ for subsequent steps.

3D Reconstruction : Find the line $\ell $ perpendicular to the xy plane that passes through the point $P_p$

where $\varvec{u}_3=\varvec{\sigma }_3 \wedge \varvec{\sigma }_{\infty }$ is the CGA representation of a free vector in direction of $\varvec{\sigma }_3$ . Now, find the plane $\varvec{\pi }_A$ perpendicular to the line $\ell $ that passes through the point A

The intersection of the line $\ell $ and the plane $\varvec{\pi }_A$ determines the point G (obtained as a flat point)

, and thus, the point at infinity must be removed using the standard formula, recovering the intersecting point G in CGA

Using the inverse map from CGA to VGA, we end up with $\vec {\varvec{g}}$ and the point of interest $\vec {\varvec{p}}$ ( P ) can be obtained as

To obtain the point P without performing the last trigonometric operation, the line AG can be rotated around A by the angle $\gamma _1$ in the plane perpendicular to the plane xy containing the line AG .

Cassini’s method when P is collinear with two points

Collins’ method when P is collinear with two points

4.4 Singularities of the methods

All three methods presented so far, i.e. VGA, Cassini CRA, and Collins CRA, encounter the same intrinsic limitation known as the dangerous circle. This issue is unavoidable with the Snellius–Pothenot formulation, where the unknown point P is part of the circle determined by the three known points. However, the graphical methods of Cassini and Collins offer distinct advantages over the VGA approach by avoiding the use of trigonometry, regardless of the challenges posed by singularities. This simplifies certain computational aspects and potentially enhances the geometric intuition behind the solutions, providing a more straightforward path to address the resection problem in specific scenarios.

For example, the angles $\alpha $ and $\beta $ in the denominators of Eq. ( 15 ) play a crucial role in the VGA method. If either angle is zero, then the result is infinity (meaning that point P lies on line segment AB or BC ). This is a common issue in all traditional methods where some trigonometric formulation is used [see Pierlot and Van Droogenbroeck ( 2014 ) for details]. To mitigate this effect in the VGA method, different reference stations can be selected to avoid zero values for $\alpha $ or $\beta $ .

In contrast, the Cassini CRA method can elegantly solve this issue graphically. Moreover, the CRA formulation also manages to capture the simplicity of the geometric solution. Figure 9 a shows the specific situation where the point P is collinear with AB (a similar case occurs for collinearity with BC , see Fig. 9 b). In either case, one of the circles degenerates into a line, and the solution simply consists of intersecting this line with the remaining circle. This is a clear example of how to deal with the singularities inherent in the trigonometric formulation by leveraging the basic principles of planar geometry. This provides a more intuitive approach to handling special alignments compared to ad hoc fixes needed for traditional resection techniques. It should be noted that no singularity occurs if P is collinear with the segment AC .

Interestingly, the Collins method presents an additional singularity beyond that of the Cassini method, occurring when the point P is collinear with segment AC .

The singularity due to the alignment of P with the sides AB or BC is solved as shown in Fig. 10 . Essentially, the point P is obtained from the intersection of the line passing through A and B and another line built by rotating line AC around C by an angle equal to $\gamma _1=\theta -\beta $ (or rotating AC around A by $\gamma _2=\varphi -\alpha $ if alignment occurs with BC ). This elegant geometric construction circumvents the infinity values that arise in the trigonometric formulation when P aligns with any side of the triangle ABC . The Collins CRA approach thereby extends the advantages of the Cassini method to fully address all possible singular configurations through basic planar geometry principles.

Finally, the singularity caused by the collinearity between P and AC is solved as follows. Note that in this situation, the rotated lines $\ell _{AE}$ and $\ell _{CE}$ are parallel as in Fig. 11 . We can recognise this by the fact that the projection of the flat point ( 38 ) is not a point, but a direction at infinity. Footnote 2 However, the search line is then characterised by the point B and the directional vector $\varvec{u}=(\varvec{\sigma }_4 \wedge \varvec{\sigma }_3) \cdot \varvec{L}_{AE}$ , that is, $\varvec{L}_{BE}=\varvec{b} \wedge \varvec{u} \wedge \varvec{\sigma }_{\infty }$ . The point we are looking for is $\varvec{P}= \varvec{L}_{BE} \vee \varvec{L}_{AC}$ , which is a flat point originating from the wedge product of our sought point P and the point at infinity $\varvec{P}=\varvec{p}\wedge \varvec{\sigma }_{\infty }$ .

5 Numerical simulations and benchmarks

5.1 two-dimensional example.

Both the VGA and CGA approaches detailed in Sects. 4.1 and 4.2 , respectively, have been implemented using specific GA software to address the 2D resection problem. Clifford (Hadfield et al. 2021 ) and GA-FuL (Eid [36]) packages were used to facilitate the work with GA. The algorithms we devised have been uploaded to GitHub, accessible via the following link: https://github.com/jorgeven98/Resection-Problem-3D . These algorithms were rigorously tested using various configurations, as illustrated in Fig. 12 . The locations of the known points, as well as the angles $\alpha $ and $\beta $ , can be retrieved from the code shared on GitHub in every instance. Remarkably, GA-based methods enable us to precisely solve any initial point arrangement.

Singular position. A , P , and C aligned

Tested point configurations using triangle ABC

In Table 3 , numerical data regarding the positions of known points A , B , and C , as well as angles $\alpha $ and $\beta $ , are presented for the four scenarios. To address these cases, the coordinates of all points (including the unknown point P ) are initially established. An auxiliary mathematical function is then employed, in conjunction with these coordinates, to ascertain the angles with precision. Subsequently, this derived angular information, together with the locations of the known points, is incorporated into our computational algorithms. The primary objective is to confirm that the calculated results are consistent with the coordinates initially designated for the point P .

5.2 Three-dimensional example

To evaluate the newly developed 3D resolution method, several examples have been proposed and solved, each featuring a distinct configuration of 3D points (see Table 4 ). For the purpose of this study, we will focus on configuration a), while the remaining examples are analysed similarly.

In the first step, we convert points A , B , and C into VGA vectors

Assuming that the position of the unknown point $\vec {\varvec{p}}$ is $(6.8103,-6.6307,14.5388)$ , the values of the horizontal angles are $\alpha =-39.7471^{\circ }$ , $\beta =305.0165^{\circ }$ and the vertical angle is $\gamma _1=31.1521^{\circ }$ . It should be noted that $\alpha $ and $\beta $ are the angles between points $A_p$ and $B_p$ , and $B_p$ and $C_p$ , respectively, as seen from $P_p$ . The subscript p indicates the projection of that point in the xy plane. On the other hand, $\gamma _1$ is the angle through which A sees P measured in the plane perpendicular to the $\varvec{\sigma }_3$ axis and taking as a reference the line parallel to the xy plane. In this case, the point A has been selected, but any other point could be used.

3D visualisation for configurations b) and c) in Table 4 . a Points A , B , and C aligned. b The projections of A , B , and C in the plane xy form a triangle with P projected inside

The procedure proposed in Sect. 4.3 is followed. By projecting onto the xy plane and solving the 2D version of the problem, we obtain the following solution

The intermediate geometric objects are also computed, with the following results:

As a result, our desired point is $P=(6.8103,-6.6307, 14.5388)$ , matching the original position vector $\vec {\varvec{p}}$ .

Figure 13 shows the point configurations for examples b) and c) in Table 4 . By applying the same method as in example a), we can determine the precise location of point P , regardless of the positions of points A , B , and C with no limitations, but the unsolvable forbidden circle (all points lying in the same plane and P belonging to the circle defined by points A , B , and C ).

5.3 Benchmarks

To evaluate the computational efficiency of our GA-based algorithms, extensive benchmarking tests were performed and the results were compared with state-of-the-art methods. Our implementation, which exploits the power of code generation, has achieved superior performance, outperforming the best-known algorithms to date, such as the ToTal algorithm and the method proposed by Ligas. Moreover, sophisticated CGA-based approaches have shown excellent results and are among the most efficient in terms of execution time.

A comprehensive set of benchmarks was conducted, comparing our algorithms against top-efficient algorithms operating in the whole plane and accommodating any ordering for the known points. Each algorithm was executed $10^6$ times at random locations within the same square-shaped area used for error analysis (see next section). The tests were performed on an Intel Core i7-9700K CPU 3.60GHz (Coffee Lake) with 8 logical and 8 physical cores (8 GB RAM, Windows 11, C#,.NET SDK 8.0.102).

Our findings reveal that our VGA-based algorithm outperforms state-of-the-art methods (see Table 5 ), executing approximately 13.3% and 30% faster than the previously best-known algorithms by Pierlot with Total #1 and Total #2.

The primary advantage of our methodology and implementation is the utilisation of GA-FuL’s comprehensive code generation capabilities. These capabilities range from generating code for individual multivector operations to creating full software libraries with proper software architecture and nested folder/file structure, enabling efficient and optimised geometric algebra computations.

6 Uncertainty analysis

This section investigates the impact of measurement uncertainties on the efficacy of the proposed GA methods. Given the intrinsic presence of noise in practical measurements, it is crucial to assess the sensitivity and resilience of the method to such perturbations (Font-Llagunes and Batlle 2009a ; Pierlot and Van Droogenbroeck 2014 ).

Previous discussions have highlighted that the resection problem faces an intractable challenge within the forbidden circle defined by points A , B , and C . This limitation is inherent in the nature of the problem rather than a reflection of the methods used to solve it. Novel methodological approaches should be considered with caution as they may inadvertently introduce undesirable scenarios and singularities not covered by the original formulation of the problem. In this regard, the proposed methods handle degenerate or limiting cases in a convenient and elegant graphical way, as shown in Fig. 11 .

This study presents three approaches to address the problem of 2D and 3D resection. In order to improve the ability to evaluate the accuracy of the algorithms and determine the station position error, a new metric has been developed. Consequently, we propose three formulations that are essentially different variations of the same underlying approach, each defining the metric D based on the square of a distance to denote the proximity of the station P to the forbidden region.

VGA method : The vector $\varvec{d}$ is used as the difference between the vectors $\varvec{d}_1$ and $\varvec{d}_2$ (refer to Eq. ( 15 )). When the station P is located on the forbidden circle, the vectors $\varvec{d}_1$ and $\varvec{d}_2$ converge, resulting in a null vector $\varvec{d}$ . Therefore, minimal values of D indicate close proximity to the forbidden circle

Cassini method : The determination of D using the CGA Cassini method requires the calculation of the squared distance between the centres of the circles ${c_1}$ and ${c_2}$ (as shown in Fig. 4 ), marked by $O_1$ and $O_2$ , respectively. In situations where the station is positioned on the forbidden circle, the two circles converge, causing their centres to overlap and the intercentre distance to become 0. Thus, according to Eq. ( A3 ), D is defined as

Collins method : Similarly to the previous method, D is determined as the squared distance between two specific points. The auxiliary Collins point E and the point B are used for this purpose. They coincide when the station P is situated on the forbidden circle. The formula used to compute this distance is as follows

Error analysis for two point configurations using a square window of $2\times 2$ m.. Config #1 is an equilateral triangle, while in config #2 the points are collinear. Both configurations have been tested with standard deviation $\sigma =0.01$ and $\sigma =0.1$ . The three GA methods (VGA, CollinsCGA, and CassiniCGA) are compared based on their position error (first row) and metric 1/ D (second row), respectively

To validate the sensitivity of the proposed algorithms, a series of simulations have been proposed. The simulation framework is designed within a square area measuring 4 by 4 square metres, incorporating two unique configurations for three known points. The first configuration is an equilateral triangle, with the points located at the positions $A = (0,1)$ , $B = (-0.866, -0.5)$ , and $C = (0.866, -0.5)$ . The points in the second configuration are linearly arranged at $A = (-0.866,0)$ , $B = (0, 0)$ , and $C = (0.866, 0)$ . A spacing of 2 cm is used in each direction across the grid. At each point on the grid, the angles $\alpha $ and $\beta $ seen from P are calculated. Gaussian noise is introduced into these angles, characterised by a zero mean and two distinct standard deviations ( $\sigma $ = 0.01 degrees and $\sigma $ = 0.1 degrees). The algorithms use these modified angles as input to determine the estimated position of the unknown point. The discrepancy in position ( $\Delta d$ ) is quantified by the Euclidean distance between the exact and estimated location of the point P .

The study performs 1000 iterations for each position to determine the standard deviation of the position error. The resulting standard deviations are shown in Fig. 14 . The results for the equilateral triangle configuration, with standard deviations of $\sigma $ = 0.01 degrees and $\sigma $ = 0.1 degrees, are presented in the first and second columns, respectively. Similarly, the results for the second configuration (collinear points) are detailed in the third and fourth columns, respectively, using the same standard deviations. The figure shows the standard deviation of the position error and the mean error measure 1/ D in the first and second rows, in that order. It is important to note that the scales used in the graphic representation are not linear. To enhance the visual clarity of these images and emphasise the correlation between the position errors and our new error metric, we applied histogram equalisation to the images.

6.1 Discussion of the results

The simulations performed are in agreement with those reported in the literature and support the case studies of each of the three methods presented. Figure 14 shows the different point configurations, where the forbidden circle is clearly identifiable due to the increase in standard deviation of the position error as it is approached. Minimal errors are observed inside the circle, while errors increase with distance outside the circle. It is remarkable that the three methods provide almost identical results for the error position.

The 1/ D metric plots maintain a shape similar to the position error plots near the forbidden circle. High red values are observed as D becomes smaller, while minimum values are observed in the lines $\ell _{AB}$ and $\ell _{BC}$ in Cassini and $\ell _{AC}$ in Collins due to an increase of D (see Figs. 9 and 10 ).

Configuration 2 transforms the forbidden circle into a straight line. In this region, the error distribution is high and increases progressively with distance from the line. Because this configuration represents a degenerate situation, the case where D becomes zero does not occur. The different methods used to define D lead to overlapping points at infinity, causing D to take high values near the critical line and resulting in a minimal value for 1/ D . The metric D was chosen for configuration 2 due to this property.

All methods produce identical position error plots, indicating consistency and conformity with the results obtained by most algorithms to solve the resection problem. This confirms that the sensitivity to calculate the position of the point P , even with noisy measured angles, is independent of the method used and unique, as discussed in Pierlot and Van Droogenbroeck ( 2014 ) and Font-Llagunes and Batlle ( 2009b ). The metric 1/ D can be used as an indicator of proximity to the forbidden circle. When dealing with aligned beacons, the value of D should be used directly. In other cases, the similarity between this metric and the position error suggests that the former can approximate the latter if a function of the other problem parameters is applied.

7 Conclusions

This article presents a novel approach to solving the resection problem in two and three dimensions using conformal geometric algebra (CGA). The CGA framework allowed representing points, lines, planes, circles, and spheres in a unified mathematical structure and offered a more intuitive understanding and efficient solution to the resection problem compared to existing algebraic techniques.

The proposed method leveraged the ability of CGA to transition between different reference frames without requiring coordinate transformations. This eliminated the need for multiple calculation steps and complex algebraic manipulations that are characteristic of traditional algebraic solutions. Through extensive numerical simulations, we have demonstrated the validity and efficacy of our GA-based approach, achieving accuracy comparable to that of established algebraic techniques, while significantly improving computational efficiency and providing valuable geometric insights.

Our findings suggest that the geometric algebra framework has strong potential for solving resection-type problems not only in surveying and geodesy but also in computer graphics, robotics, computer vision, and navigation. By exploiting geometric relationships between entities, CGA paves the way for more intuitive solutions that unify computations involving different geometric primitives.

Future research can build upon the ideas presented here to address more complex variants of the resection problem that involve additional constraints. The CGA method can also be extended to address intersection problems and other spatial geometric computations across diverse disciplines. By harnessing the power of geometric algebra and the versatility of conformal geometric methods, this work opens up new possibilities for advancing geometric research and computational techniques.

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Jorge Ventura, Fernando Martinez, Francisco Manzano-Agugliaro & Francisco G. Montoya

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Appendix A Some calculations over CGA

CGA has been briefly introduced in Sect. 2.2 . In this Appendix, some fundamental calculations are presented to illustrate the computational efficiency inherent in this algebra. For further information and a detailed understanding, the reader is referred to Hrdina et al. ( 2021 ), Dorst et al. ( 2010 ), Hestenes and Sobczyk ( 2012 ), Hildenbrand ( 2018 ).

1.1 A.1 Conformal inclusion

We’ll show how the translations and rotations are connected and related to the insertion of the Euclidean space. If we choose vector $\varvec{\sigma }_0$ as the origin of the coordinate system and use the element

, then it can act as a translation, allowing us to define an inclusion as a translation of the origin $\varvec{\sigma }_0$ in the direction of the vector $\vec {\varvec{x}}=(x \varvec{\sigma }_1 + y \varvec{\sigma }_2 +z \varvec{\sigma }_3)$ by the sandwich product as

So, we see that we can identify points in $\mathbb R^3$ with vectors in CGA through the inclusion

where the element $\varvec{T}$ acts as a translation. Using a similar reasoning, the element $\varvec{R}=e^{n_1\varvec{\sigma }_2\varvec{\sigma }_3 +n_2\varvec{\sigma }_1\varvec{\sigma }_3+n_3\varvec{\sigma }_1\varvec{\sigma }_2}$ acts as a rotation due to identification $\text {Im } {\mathbb {H}} =\langle \varvec{\sigma }_2\varvec{\sigma }_3,\varvec{\sigma }_1\varvec{\sigma }_3, \varvec{\sigma }_1\varvec{\sigma }_2 \rangle $ and the following computation

1.2 A.2 Distance between points

One of the key distinctions between CGA and VGA lies in the interpretation of the inner product. In CGA, the inner product represents the distance between points, which is fundamentally a quadratic concept in VGA. By incorporating two additional dimensions, CGA linearises this quadratic function. The equation below elucidates this:

This calculation explicitly demonstrates how CGA linearises the quadratic nature of the distance representation found in VGA, offering nuanced insights into geometric relations and interactions between points.

Furthermore, this characteristic is utilised to depict the midline $\varvec{M}_{}$ as illustrated in expression ( 18 ). A midline is established by two control points, $\varvec{a}$ and $\varvec{b}$ , and encompasses points that maintain equal distances to these control points. This means that $ (\varvec{x}-\varvec{a})^2 = (\varvec{x}-\varvec{b})^2 $ . In the context of CGA, this condition can be articulated as follows:

i.e. $\varvec{x} \in \varvec{M}_{AB} \leftrightarrow \varvec{x} \cdot (\varvec{a} -\varvec{b}) =0$ , so $(\varvec{a} - \varvec{b})$ is the IPNS representation of the midline defined by control points $\varvec{a}$ and $\varvec{b}$ .

1.3 A.3 IPNS vs OPNS representation of objects

In GA, we have several types of product, so it is possible to represent objects in different ways. With the help of the inner product, we can define the object ${\mathcal {C}}$ as follows.

In CGA, for example, the object ${\mathcal {C}} = n_1 \varvec{\sigma }_1+n_2 \varvec{\sigma }_2 +n_3 \varvec{\sigma }_3 + d \varvec{\sigma }_{\infty }$ can be tested and verify that it represents a plane

where $\vec {\varvec{n}} = n_1 \varvec{\sigma }_1+n_2 \varvec{\sigma }_2+n_3 \varvec{\sigma }_3$ . Equation ( A5 ) describes a plane with normal vector $\vec {\varvec{n}}$ and distance from the origin d . On the other hand, the wedge product defines an object ${\mathcal {D}}$ as follows

Again, in CGA, for example, the object

defines the line goes through the points $\varvec{a}$ and $\varvec{b}$ :

which represented the line based on the points $\varvec{a}$ and $\varvec{b}$ .

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Ventura, J., Martinez, F., Manzano-Agugliaro, F. et al. A novel geometric method based on conformal geometric algebra applied to the resection problem in two and three dimensions. J Geod 98 , 47 (2024). https://doi.org/10.1007/s00190-024-01854-1

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Received : 05 October 2023

Accepted : 23 April 2024

Published : 27 May 2024

DOI : https://doi.org/10.1007/s00190-024-01854-1

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Prompt Engineering

Latest Modern Advances in Prompt Engineering: A Comprehensive Guide

Prompt engineering , the art and science of crafting prompts that elicit desired responses from LLMs, has become a crucial area of research and development.

From enhancing reasoning capabilities to enabling seamless integration with external tools and programs, the latest advances in prompt engineering are unlocking new frontiers in artificial intelligence. In this comprehensive technical blog, we'll delve into the latest cutting-edge techniques and strategies that are shaping the future of prompt engineering.

Advanced Prompting Strategies for Complex Problem-Solving

While CoT prompting has proven effective for many reasoning tasks, researchers have explored more advanced prompting strategies to tackle even more complex problems. One such approach is Least-to-Most Prompting, which breaks down a complex problem into smaller, more manageable sub-problems that are solved independently and then combined to reach the final solution.

Another innovative technique is the Tree of Thoughts (ToT) prompting, which allows the LLM to generate multiple lines of reasoning or “thoughts” in parallel, evaluate its own progress towards the solution, and backtrack or explore alternative paths as needed. This approach leverages search algorithms like breadth-first or depth-first search, enabling the LLM to engage in lookahead and backtracking during the problem-solving process.

Integrating LLMs with External Tools and Programs

While LLMs are incredibly powerful, they have inherent limitations, such as an inability to access up-to-date information or perform precise mathematical reasoning. To address these drawbacks, researchers have developed techniques that enable LLMs to seamlessly integrate with external tools and programs.

One notable example is Toolformer, which teaches LLMs to identify scenarios that require the use of external tools, specify which tool to use, provide relevant input, and incorporate the tool's output into the final response. This approach involves constructing a synthetic training dataset that demonstrates the proper use of various text-to-text APIs.

Another innovative framework, Chameleon, takes a “plug-and-play” approach, allowing a central LLM-based controller to generate natural language programs that compose and execute a wide range of tools, including LLMs, vision models, web search engines, and Python functions. This modular approach enables Chameleon to tackle complex, multimodal reasoning tasks by leveraging the strengths of different tools and models.

Fundamental Prompting Strategies

Zero-shot prompting.

Zero-shot prompting involves describing the task in the prompt and asking the model to solve it without any examples. For instance, to translate “cheese” to French, a zero-shot prompt might be:

This approach is straightforward but can be limited by the ambiguity of task descriptions.

Few-Shot Prompting

Few-shot prompting improves upon zero-shot by including several examples of the task. For example:

This method reduces ambiguity and provides a clearer guide for the model, leveraging the in-context learning abilities of LLMs.

Instruction Prompting

Instruction prompting explicitly describes the desired output, which is particularly effective with models trained to follow instructions. For example:

Models like GPT-4 have been specifically fine-tuned to follow such instructions accurately.

Advanced Prompting Techniques

Enhancing reasoning capabilities with chain-of-thought prompting.

One of the most significant breakthroughs in prompt engineering has been the development of Chain-of-Thought (CoT) prompting . This technique aims to elicit and improve the reasoning capabilities of LLMs by encouraging them to generate a step-by-step thought process or rationale before providing the final answer.

Left: Traditional methods of prompting LLMs rely on generic inputs (0-shot CoT) or necessitate labeled examples (few-shot CoT). Right: The novel approach prompts LLMs to self-create relevant examples prior to problem-solving, removing the need for labeling while customizing examples to each unique problem

CoT prompting works by presenting the LLM with examples that include not only the input and output but also the intermediate reasoning steps or “chain of thought” that leads to the solution. By learning from these exemplars, the LLM can then generate its own chain of thought when presented with new problems, improving its ability to tackle complex reasoning tasks.

Input: Natalie has 3 apples, and she wants to share them equally with her 2 friends. How many apples will each person get? Chain of Thought: Okay, let's break this down step-by-step:

Natalie has 3 apples
She wants to share them equally with 2 friends
So there are 3 people in total (Natalie and her 2 friends)
To share the apples equally, we divide the total number of apples (3) by the number of people (3)
3 divided by 3 is 1
Therefore, each person will get 1 apple. Output: Each person will get 1 apple.

By explicitly generating the reasoning process, LLMs like GPT-3 and Codex have demonstrated significant improvements in arithmetic, commonsense, and symbolic reasoning tasks.

Self-Consistency

Self-consistency improves the reliability of CoT prompting by generating multiple chains of thought and taking a majority vote on the final answer. This method mitigates the impact of any single incorrect reasoning path.

Least-to-Most Prompting

Least-to-most prompting breaks down complex problems into simpler sub-problems, solving each one sequentially and using the context of previous solutions to inform subsequent steps. This approach is beneficial for multi-step reasoning tasks.

Recent Advances in Prompt Engineering

Prompt engineering is evolving rapidly, and several innovative techniques have emerged to improve the performance of large language models (LLMs). Let's explore some of these cutting-edge methods in detail:

Auto-CoT (Automatic Chain-of-Thought Prompting)

What It Is: Auto-CoT is a method that automates the generation of reasoning chains for LLMs, eliminating the need for manually crafted examples. This technique uses zero-shot Chain-of-Thought (CoT) prompting, where the model is guided to think step-by-step to generate its reasoning chains.

How It Works:

Zero-Shot CoT Prompting: The model is given a simple prompt like “Let's think step by step” to encourage detailed reasoning.
Diversity in Demonstrations: Auto-CoT selects diverse questions and generates reasoning chains for these questions, ensuring a variety of problem types and reasoning patterns.

Advantages:

Automation: Reduces the manual effort required to create reasoning demonstrations.
Performance: On various benchmark reasoning tasks, Auto-CoT has matched or exceeded the performance of manual CoT prompting.

Complexity-Based Prompting

What It Is: This technique selects examples with the highest complexity (i.e., the most reasoning steps) to include in the prompt. It aims to improve the model's performance on tasks requiring multiple steps of reasoning.

Example Selection: Prompts are chosen based on the number of reasoning steps they contain.
Complexity-Based Consistency: During decoding, multiple reasoning chains are sampled, and the majority vote is taken from the most complex chains.
Improved Performance: Substantially better accuracy on multi-step reasoning tasks.
Robustness: Effective even under different prompt distributions and noisy data.

Progressive-Hint Prompting (PHP)

What It Is: PHP iteratively refines the model’s answers by using previously generated rationales as hints. This method leverages the model's previous responses to guide it toward the correct answer through multiple iterations.

Initial Answer: The model generates a base answer using a standard prompt.
Hints and Refinements: This base answer is then used as a hint in subsequent prompts to refine the answer.
Iterative Process: This process continues until the answer stabilizes over consecutive iterations.
Accuracy: Significant improvements in reasoning accuracy.
Efficiency: Reduces the number of sample paths needed, enhancing computational efficiency.

Decomposed Prompting (DecomP)

What It Is: DecomP breaks down complex tasks into simpler sub-tasks, each handled by a specific prompt or model. This modular approach allows for more effective handling of intricate problems.

Task Decomposition: The main problem is divided into simpler sub-tasks.
Sub-Task Handlers: Each sub-task is managed by a dedicated model or prompt.
Modular Integration: These handlers can be optimized, replaced, or combined as needed to solve the complex task.
Flexibility: Easy to debug and improve specific sub-tasks.
Scalability: Handles tasks with long contexts and complex sub-tasks effectively.

Hypotheses-to-Theories (HtT) Prompting

What It Is: HtT uses a scientific discovery process where the model generates and verifies hypotheses to solve complex problems. This method involves creating a rule library from verified hypotheses, which the model uses for reasoning.

Induction Stage: The model generates potential rules and verifies them against training examples.
Rule Library Creation: Verified rules are collected to form a rule library.
Deduction Stage: The model applies these rules to new problems, using the rule library to guide its reasoning.
Accuracy: Reduces the likelihood of errors by relying on a verified set of rules.
Transferability: The learned rules can be transferred across different models and problem forms.

Tool-Enhanced Prompting Techniques

Toolformer integrates LLMs with external tools via text-to-text APIs, allowing the model to use these tools to solve problems it otherwise couldn't. For example, an LLM could call a calculator API to perform arithmetic operations.

Chameleon uses a central LLM-based controller to generate a program that composes several tools to solve complex reasoning tasks. This approach leverages a broad set of tools, including vision models and web search engines, to enhance problem-solving capabilities.

GPT4Tools finetunes open-source LLMs to use multimodal tools via a self-instruct approach, demonstrating that even non-proprietary models can effectively leverage external tools for improved performance.

Gorilla and HuggingGPT

Both Gorilla and HuggingGPT integrate LLMs with specialized deep learning models available online. These systems use a retrieval-aware finetuning process and a planning and coordination approach, respectively, to solve complex tasks involving multiple models.

Program-Aided Language Models (PALs) and Programs of Thoughts (PoTs)

In addition to integrating with external tools, researchers have explored ways to enhance LLMs' problem-solving capabilities by combining natural language with programming constructs. Program-Aided Language Models (PALs) and Programs of Thoughts (PoTs) are two such approaches that leverage code to augment the LLM's reasoning process.

PALs prompt the LLM to generate a rationale that interleaves natural language with code (e.g., Python), which can then be executed to produce the final solution. This approach addresses a common failure case where LLMs generate correct reasoning but produce an incorrect final answer.

Similarly, PoTs employ a symbolic math library like SymPy, allowing the LLM to define mathematical symbols and expressions that can be combined and evaluated using SymPy's solve function. By delegating complex computations to a code interpreter, these techniques decouple reasoning from computation, enabling LLMs to tackle more intricate problems effectively.

Understanding and Leveraging Context Windows

LLMs' performance heavily relies on their ability to process and leverage the context provided in the prompt. Researchers have investigated how LLMs handle long contexts and the impact of irrelevant or distracting information on their outputs.

The “Lost in the Middle” phenomenon highlights how LLMs tend to pay more attention to information at the beginning and end of their context, while information in the middle is often overlooked or “lost.” This insight has implications for prompt engineering, as carefully positioning relevant information within the context can significantly impact performance.

Another line of research focuses on mitigating the detrimental effects of irrelevant context, which can severely degrade LLM performance. Techniques like self-consistency, explicit instructions to ignore irrelevant information, and including exemplars that demonstrate solving problems with irrelevant context can help LLMs learn to focus on the most pertinent information.

Improving Writing Capabilities with Prompting Strategies

While LLMs excel at generating human-like text, their writing capabilities can be further enhanced through specialized prompting strategies. One such technique is Skeleton-of-Thought (SoT) prompting, which aims to reduce the latency of sequential decoding by mimicking the human writing process.

SoT prompting involves prompting the LLM to generate a skeleton or outline of its answer first, followed by parallel API calls to fill in the details of each outline element. This approach not only improves inference latency but can also enhance writing quality by encouraging the LLM to plan and structure its output more effectively.

Another prompting strategy, Chain of Density (CoD) prompting, focuses on improving the information density of LLM-generated summaries. By iteratively adding entities into the summary while keeping the length fixed, CoD prompting allows users to explore the trade-off between conciseness and completeness, ultimately producing more informative and readable summaries.

Emerging Directions and Future Outlook

Advanced Prompt Engineering

The field of prompt engineering is rapidly evolving, with researchers continuously exploring new frontiers and pushing the boundaries of what's possible with LLMs. Some emerging directions include:

Active Prompting : Techniques that leverage uncertainty-based active learning principles to identify and annotate the most helpful exemplars for solving specific reasoning problems.
Multimodal Prompting : Extending prompting strategies to handle multimodal inputs that combine text, images, and other data modalities.
Automatic Prompt Generation: Developing optimization techniques to automatically generate effective prompts tailored to specific tasks or domains.
Interpretability and Explainability: Exploring prompting methods that improve the interpretability and explainability of LLM outputs, enabling better transparency and trust in their decision-making processes.

As LLMs continue to advance and find applications in various domains, prompt engineering will play a crucial role in unlocking their full potential. By leveraging the latest prompting techniques and strategies, researchers and practitioners can develop more powerful, reliable, and task-specific AI solutions that push the boundaries of what's possible with natural language processing.

The field of prompt engineering for large language models is rapidly evolving, with researchers continually pushing the boundaries of what's possible. From enhancing reasoning capabilities with techniques like Chain-of-Thought prompting to integrating LLMs with external tools and programs, the latest advances in prompt engineering are unlocking new frontiers in artificial intelligence.

What is Chain-of-Thought (CoT) Prompting? Examples & Benefits

I have spent the past five years immersing myself in the fascinating world of Machine Learning and Deep Learning. My passion and expertise have led me to contribute to over 50 diverse software engineering projects, with a particular focus on AI/ML. My ongoing curiosity has also drawn me toward Natural Language Processing, a field I am eager to explore further.

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