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Tue Sep 18 15:26:42 PDT 2007

# Polya - how to solve it

## Source

1. Princeton 1988 2nd edn isbn0-691-02356-5 QA11P6 1988 [Polya88]

## Overview

1. Understand, 2. Plan, 3. Carry_out_the_plan, 4. Looking_Back.

## Details

### Understand

1. What is the unknown? -- goal/output/conclusion?
2. What are the data? -- given/input/parameters/hypothesis
3. What are the conditions? -- operations/relations/premises connect/ given to goal
4. Check conditions: possible & sufficient ~ redundant~ contradictory ~ separate
5. Draw a diagram.
6. Introduce a suitable notation.
7. Separate the various parts of the condition. Can you write them down?

### Plan

8. Use plausible, reversed, and lateral thinking to invent a way to solve the problem. Avoid rigor and details.
9. Look at the goal/end point first!
10. Have you seen a similar problem before?
• Look for similar goal/given/...
• Look for more general/specific.
• Look at any previously solved problem/theorem... can you make use of it?
11. Can you restate/reverse ths problem?
12. Review
1. Did you use all the data/givens?
2. did you use the whole condition?
3. Have you allowed all the notions in the problem... if not revise your plan.

### Carry_out_the_plan

13. Carry out your plan step by rigorous step.
14. Fill in the details in steps top-down by refinement.+
15. At each step look for signs of progress,
16. Check each step for correctness.
• Can you see that it is correct(intuitive)?
• Use formal techniques that fill in the details in your plan.+
• Can you prove that it is correct?

### Looking_Back

17. Can you check the result?
18. Can you check the steps?
19. Did you use all the givens?
20. Can you improve the steps?
21. Can you see the whole at a glance?
22. Can you use the result or the method in some other probleme?
23. How can you share/present/publish the result? +

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