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         Poyla’s Recipe for Problem Solving: An Overview

 

          From: Polya, George. How to solve it. (Princeton 1945).

 

 

 

Label for Step

 

Focus of Step

 

Things to Consider

 

Helpful Procedures

 

1. Understanding the Problem

 

You have to understand the problem.

 

a)      What is the unknown?

b)      What are the data?

c)      What is the condition?

Is it possible to satisfy the condition?

 

Is the condition sufficient to determine the unknown?

 

It is insufficient? Or redundant? Or contradictory?

Draw a figure.

 

Introduce suitable notation.

 

Separate the various parts of the condition.

2. Devising a Plan

Find the connection between the data and the unknown.

Have you seen the same problem in a slightly different form?

 

Do you know a related problem? Or a theorem that could be helpful?

Look at the unknown!

 

Try to think of a familiar problem having the same or similar unknown.

3. Carrying out the Plan

Carrying out your plan of the solution, check each step.

Can you see clearly that each step is correct?

Can you prove that each step is correct?

4. Looking Back

Examine the solution you obtained.

a)      Can you check the result?

b)      Can you check the argument?

Can you derive the result differently?

 

Can you see the result at a glance?

 

 

Can you use the result, or the method, for some other problem?

 

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