- Polya - how to solve it
- : Source
- : Overview
- : Details
- : : Understand
- : : Plan
- : : Carry_out_the_plan
- : : Looking_Back

- 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

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

- Use plausible, reversed, and lateral thinking to invent a way to solve the problem. Avoid rigor and details.
- Look at the goal/end point first!
- 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?

- Can you restate/reverse ths problem?
- Review
- Did you use all the data/givens?
- did you use the whole condition?
- Have you allowed all the notions in the problem... if not revise your plan.

### Carry_out_the_plan

- Carry out your plan step by rigorous step.
- Fill in the details in steps top-down by refinement.+
- At each step look for signs of progress,
- 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

- Can you check the result?
- Can you check the steps?
- Did you use all the givens?
- Can you improve the steps?
- Can you see the whole at a glance?
- Can you use the result or the method in some other probleme?
- How can you share/present/publish the result? +

### Understand

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