How To Solve It

Taken from the book How to Solve It

Use this list of questions to help solve any problem you come across. The more these questions help you, the more you're likely to assimilate them into your problem-solving toolkit.

Understanding the Problem

First, you have to understand the problem.

1. What is the unknown?

2. What are the data?

3. What is the condition? Is it possible to satisfy the condition? Is the condition sufficient to determine the unknown? Is the condition insufficient? redundant? contradictory?

   • Separate the various parts of the condition. Can you write them down?

Devising a Plan

Second, you have to find the connection between the data and the unknown. Try looking at different but similar problems to ultimately come up with a plan.

1. Have you seen the problem before in a similar form?

2. Do you know a related problem?

3. Look at the unknown and find a problem with a similar unknown (preferably already solved).

   • Could you use the solution to this problem to solve your problem?

   • If not the solution, could you at least use it's method?

   • change the problem slightly in order to make it useful to you

4. Could you restate the problem? Restate it again but differently.

5. Could you imagine a more general or more specific problem?

6. Can you solve a part of the problem?

7. Keep only a part of the condition. Can you solve the problem now?

8. How can the unknown vary?

9. Could you derive something useful from the data?

10. Could you think of other data appropriate to determine the unknown?

11. Could you change the data or the unknown (or both) to make them nearer to each other?

12. Did you use all the data? Did you use the whole condition?

Carry out a Plan

Check each step in your plan and carry it out.

1. Can you see clearly that the step is correct?

2. Can you prove that each step is correct?

Look Back

Take time to look back on the solution that was devised and carried out. Examine it with scrutiny. Reflection is the best way learn from your mistakes.

1. Can you verify the result? Double check the problem statement.

2. Can you derive the result differently now that you have at least one solution?

3. Can you see the solution at a glance?

4. Can you use the result or the method of this solution to solve some other problem you've encountered? Use this solution as a sub solution to a bigger problem.