How to Solve It
By George Pólya (1945)
Do you know a related problem?
Auxiliary problem is a problem which we consider, not for its own sake, but because we hope that its consideration may help us to solve another problem, our original problem.
Can you check the result? Can you check the argument?
Can you derive the result differently?
Can you use the result, or the method, for some other problem?
Could you restate the problem? Could you restate it still differently?
To solve a serious scientific problem, will power is needed that can outlast years of toil and bitter disappointments.
Have you seen it before?
There are certain moments in which it is better to leave the problem alone for a while.
The hen that doesn’t go back around the fence to reach its goal:
No, we should not even blame the hen for her clumsiness. There is a certain difficulty in turning round, in going away from the goal, in proceeding without looking continually at the aim, in not following the direct path to the desired end. There is an obvious analogy between her difficulties and our difficulties.