Thinking Skills

30+ Most Useful Problem Solving Methods

Problem solving skills

If you’re not part of the solution, then you’re a part of the problem.

- Eldridge Cleaver, the Black Panthers


Everything has been thought of before, but the problem is to think of it again.

- Johann W. von Goethe


For every complex problem, there is a solution that is simple, neat, and wrong.

- H.L. Mencken


Nine concepts to keep in mind before you set out to solve the problem


- Research: Study what others have written about the problem (and related problems). Maybe there's already a solution?

- Assumption reversal: Write down your assumptions about the problem, and then reverse them all.

- Analogy: Has a similar problem (possibly in a different field) been solved before?

- Hypothesis testing: assuming a possible explanation to the problem and trying to prove the assumption.

- Constraint examination: are you assuming a constraint which doesn't really exist?

- Take more time: time pressure can cause one to think in circles (the brain, unhelpfully, tends to be 'pulled' towards a particular solution, or aspect of the problem)

- Incubation: input the details of a problem into your mind, then stop focusing on it. The subconscious mind will continue to work on the problem, and the solution might just 'pop up' while you are doing something else

- Build (or write) one or more abstract models of the problem

- Try to prove that the problem cannot be solved. Where the proof breaks down can be your starting point for resolving it



30+ Most Useful Problem solving methods:


1. The basics of problem solving is simple enough:

Identify the problem

Define the problem

Examine the options

Act on a plan

Look at the consequences

Put the solution into practice and check the results


2. The Feynman Problem-Solving algorithm

- Write down the problem;

- Think very hard;

- Write down the answer.


- Attributed to Murray Gell-Mann (This approach can also be summarized as, 'What one fool can do, another can too.'. Richard Feynman, the Nobel prize winning physicist was known for his approachability)


3. Root Cause Analysis Using 'The Five Whys'

This is also known as the Toyota method, which five whys to get to the root cause of an issue, each of the whys resulting on the answer given to the previous 'why'.


4. Cause and effect diagrams

- What is the problem?

- List the major factors

- List the possible causes for each


5. Affinity diagrams

- Used often in project management, where people suggest ideas and solutions in brainstorming solutions

- The all these ideas are organized into similar themes

- Then these 'idea sets' are discussed


6. The 4 D approach

- Define the problem: What do you need to find out? What do you know? What would be a reasonable estimation?

- Develop a plan (what might be, brainstorm ideas, find strategies? What tools/people/etc would you need?)

- Do the problem

- Deliver


7. Stakeholder analysis

Analyzing how each main group will be affected by your decision.


Step 1: List all potentially affected parties - The affected community, decision makers, customers, industry in which the business operates, shareholders, bondholders, suppliers and their industry, employees and their families, social interest groups (industrial, consumer, environmental, political, unions). The list may be longer. At the analysis stage the list is narrowed to the significant players, then a situational analysis is performed, and eventually a decision is reached.

Step 2: Evaluate all the ‘harms’ and ‘benefits’.

Step 3: Determine each of the affected parties’ ‘Rights’ and ‘Responsibilities’.


For example, employees have the right to a fair wage and safe working conditions, but they also have the responsibility to be productive for the company.


Also, differentiate between stakeholders directly and indirectly affected by the problem/decision.


8. The Flow chart method

- Used for understanding process flows

- Rectangles show instructions or actions

- Diamonds show decisions that must be made


9. Risk analysis and risk management

- Identify the threats (human, operational, reputational, procedural, project, financial, technical, natural, political, others)

- Estimate the risk (probability of an event occurring, cost impact)

- Manage risk (contingency planning, plan B, use existing resources, get more resources)

- Review


10. Hill-climbing strategy

- Attempting at every step to move closer to the goal situation (choosing an alternative that gets us closer). Some say the problem with this is after a number of shifts up, people may tend to forget the main, focusing on choosing the next best step instead.


11. What would (insert name of your idol/famous figure) do?

How would Warren Buffet solve this business problem, for example?


12. Means-end analysis

More effective than hill-climbing, requires the setting of sub-goals based on the process of getting from the initial state to the goal state when solving a problem.


13. Working backwards

A visualization technique. See yourself having solved the problem and people are reaping the benefits. How did that happen? What did you do? Write it down, backwards - 'I must have...then I must have...'


14. Trial-and-error

As it says on the sticker. Trial and error. Learning by doing.


15. Brainstorming: Group creativity exercise where people are encouraged to suggest ideas/solutions.


Techniques related to Brainstorming:

- Brain Writing: It is brainstorming using the chain method. People write their ideas on their own sheet of paper. Then the sheets are redistributed and other people riff upon ideas given by other people, creating an even larger number of ideas/solutions.


- Nominal group technique (prioritizing issues to achieve consensus)

- Multi voting (voting on all the issues)

- Charlotte procedure (brainstorming many issues with many people)

- Delphi technique (achieving consensus among experts)

- Concept attainment (reaching a shared understanding of issues)

- Role playing (preparing for difficult problems)


16. Wind Tunnel: based on Socratic Method whereby you outrun your logical constraints to reach for new insights to a problem.


17. Deductive reasoning: The kind of reasoning in which the conclusion is necessitated by, or reached from, previously known facts (the premises). If the premises are true, the conclusion must be true.


18. Random stimulus: A class of creativity techniques that explore randomization.

For example, 'The oblique strategies' created by Brian Eno and Peter Schmidt in 1975 is a set of 100 cards, each of which is a suggestion of a course of action or thinking to assist in creative situations, where standard logical solutions don't produce a desired result


19. Association: A widely used memory tool. Associating a new item (an object, a picture, a smell or anything else a person may wish to recall) to another, more easily-remembered item can allow you to think of them both.


20. Association of ideas: The theory of the association of ideas is the name of a theory first propounded by Aristotle, where he identified three contexts in which ideas might be associated.

The three contexts are:

- Similarity

- Contrast

- Contiguity in time or space


21. Ideas bank: A repository (on your company intranet) where people post, exchange, discuss, and polish new ideas. Some of ideas banks for the purpose of developing new inventions or technologies


22. Imagination: The process of forming in the mind new images which have not been previously experienced, or at least only partially or in different combinations. Some typical examples follow:

- Fairy tales

- Fiction

- A form of verisimilitude often invoked in fantasy and science fiction invites readers to pretend such stories are true by referring to objects of the mind such as fictional books or years that do not exist apart from an imaginary world.


23. Free association: The mind is allowed to roam over broad territory by linking one word, idea or a concept with another in a chain. It can be a highly focused activity or a general way of explaining alternatives


24. Checklists: These ensure that we look at the problem or situation more systematically. They work best for straightforward situations.


25. Role Playing: Fresh insights are often gained into existing situations. It works well when trying to identify new alternatives. It helps you gain people’s commitment to decisions and triggering new thinking


26. Drawing: It helps us get in touch with a part of our brain that may not actually have a chance to contribute to a decision.


How to solve problems by drawing pictures: Next time you face a business problem, try this


1. Draw a small circle in the middle of a page and label it 'my business' (or 'me').

2. Now, off to one side, draw a larger second circle, and call it 'my customers'.

3. Draw an arrow between the circles, and label it 'my sales channel'.

4. Add a few words describing that channel: is it 'good', 'needs improvement', 'solid', 'stretched', etc.

5. On the other side of the 'my customer' circle, draw a third circle and call it 'my competitor'.

6. Is this circle bigger than yours? Is it closer to your customers, or further away? Think about what you're starting to see here in the relationships of these circles, and note down any thoughts that occur.

7. Draw an arrow between 'competitor' and 'customer' and describe that channel.


(Source: 'The Back of the Napkin: Solving Problems and Selling Ideas with Pictures' by Dan Roam)


27. Metaphors, Analysis and Images: These can redefine the problem or decision. For example, seeing a company’s takeover attempt as an 'attack' may provide powerful new insights into choices before you.


28. The 8-Step Simplex Method


- What is the problem?

- Get the facts - all the facts.

- Ask yourself: Why did the problem arise? What’s stopping you?

- Generate ideas to solve the problem.

- Select the best solution & evaluate it: Use the Six thinking Hats or do a Cost/Benefit exercise.

- Plan how will you implement the solution.

- Sell your solution to others: If there are other people involved in the process - your boss, for example.

- Do it now - implement your solution.



Useful when you want to explore possibilities around a goal or idea. It's good for turning a tired idea into something new and different.


Write your goal at the top of the page and then SCAMPER; apply each word one at a time to your idea and see how many new possibilities you can come up with. Write them down.


Substitute: e.g. What else instead? Who else instead? Other material? Other place?


Combine: e.g. How about a blend? Combine purposes? Combine appeals?


Adapt: e.g. What else is like this? What other idea does this suggest? What could I copy?


Minify/Magnify: e.g. Order, form, shape? What to add? More time? Greater frequency? Higher? Longer? Thicker?


Put to other uses: e.g. New ways to use as is? Other uses I modified? Other places to use? Other people to reach?


Eliminate: e.g. What to subtract? Smaller? Condensed? Miniature? Lower? Shorter? Lighter? Leave something out? Streamline? Understate?


Reverse/Rearrange: e.g. Other pattern? Other layout? Other sequence? Change pace? Swap positive and negative? How about opposites? Turn it backward? Turn it upside-down? Reverse roles?


30. Critical Path Analysis: It basically consists of writing down all the activities of a project; showing how these activities are related to each other; examine all parts of the project and analyze its constituent parts.


This helps you decide both what needs to be done and in what order. By viewing the interdependencies you can choose the most effective one.


The sequence of activities that completes the project in the least time is called the Critical Path. Any delay in completing the tasks on this path will cause the project to be delayed.


31. How to Solve It: George Pólya's 1945 book 'How to Solve It' suggests the following steps when solving a mathematical problem:


- First, you have to understand the problem.

- After understanding, then make a plan.

- Carry out the plan.

- Look back on your work. How could it be better?


If this technique fails, Polya advises: 'If you can't solve a problem, then there is an easier problem you can solve: find it.' Or: 'If you cannot solve the proposed problem try to solve first some related problem. Could you imagine a more accessible related problem?'


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