The following guide takes after G. Polya's writings about how a mathematician thinks. Even though the topic is logic, the discovery and solution of mathematical problems involves induction and heuristic thinking.

1 Understand the problem

- What is the unknown?
- What are the data?
- What is the condition?
- Can the problem be solved?

- What can you or need you assume?
- What shouldn't you assume?
- Have you made subconscious assumptions?

- Have you seen this or a related problem before?
- Have you seen a similar unknown before?
- Can you restate the problem?
- If you can't solve this problem, can you solve a similar or simpler problem?

- Are you sure of the solution? Can you see it at a glance?
- Did you use all the data? the whole condition?
- Can you get the same solution another way?
- Are there other valid solutions?
- Can you apply the solution or method to another problem?
- Was this a satisfying problem to solve?

G. Polya's Plan of Attack