Problem solving guide

Summary

An adaptation of "How to solve it" by G. Polya

What are the unknowns/variables? What are the data? What is the condition (How can it be reproduced)?
What were the assumptions made?
Is it possible to satisfy the condition? Is the condition sufficient to determine the unknown? Or is it insufficient? Or redundant? Or contradictory?
Draw a figure. Visualise links between the different parts and how they might interact.
Separate the various parts of the condition. Can you write them down?
Can you diagram seperate states and try to find the path to each?

Find a connection between the data and the unknowns.
You may be obliged to consider auxiliary problems if an immediate connection cannot be found.
Have you seen this 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?
Look at the unknown! And try to think of a familiar problem having the same or a similar unknown.
Here is a problem related to yours and solved before. Could you use it? Could you use its result? Could you use its method? Should you introduce some auxiliary element in order to make its use possible?
Could you restate the problem? Could you restate it still differently? Go back to definitions.
If you cannot solve the proposed problem try to solve first some related problem. Could you imagine a more accessible related problem? A more general problem? A more special problem? An analogous problem?
Could you solve a part of the problem? Keep only a part of the condition, drop the other part; how far is the unknown then determined, how can it vary?
Could you derive something useful from the data? Could you think of other data appropriate to determine the unknown? Could you change the unknown or data, or both if necessary, so that the new unknown and the new data are nearer to each other?
Did you use all the data? Did you use the whole condition? Have you taken into account all parts involved in the problem?