Heuristic Problem Solving

A summary of Polya's 'How to Solve It' List;

First.

You have to understand the problem

What is unknown?

What are the data?

What is the condition?

.......

Second.

Find a connection between the data and the unknown

You maybe obliged to consider auxiliary problems if an immediate connection cannot be found

You should obtain eventually a plan of the solution


Have you seen it before?

Do you know a related problem?

Look at the unknown

Third.

Carry out your plan.

Check each step.

Can you see clearly that the step is correct?

Can you prove it is correct?

Fourth.

Examine the solution obtained

Can you check the result?

Can you check the argument?

Can you derive the result differently?

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

Heuristics

From Greek heuriskein, to discover, find. Related to "eureka," which is used to express triumph upon finding or discovering something. From Greek heurika, "I have found (it)" (ostensibly exclaimed by Archimedes when, while bathing, he discovered the means of measurement of volume of an irregular solid by the displacement of water, and thus was able to determine the purity of a gold crown belonging to the tyrant of Syracuse).

A reservoir may rightly feel like making such an exclamation when they establish the key reservoir characteristic influencing a history-match.