HOW TO SOLVE IT

G. Polya

1. UNDERSTANDING THE PROBLEM

You have to understand the problem.

What is the unknown? What are the data? What is the condition?

Is it possible to satisfy the condition? Is the condition sufficient to determine the unknown? Or is it insufficient? Or redundant? Or contradictory?

2. DEVISING A PLAN

Find the connection between the data and the unknown.

Have you seen it before? Or have you seen the same problem in a slightly different form? Do you know a related problem? Do you know a theorem that could be useful? Here is a Problem related to yours and solved before. Could you use it?

Could you derive something useful from the data? Could you think of other data appropriate to determine the unknown?

3. CARRYING OUT THE PLAN

Carry out your plan.

Carrying out your plan of the solution, check each step. Can you see clearly that the step is correct? Can you prove that it is correct?

4. LOOKING BACK

Examine the solution obtained.

Can you check the result? Can you check the argument? Can you derive the result differently? Can you see it at a glance? Can you use the result, or the method, for some other problem?