Ian recalls some of the basic problem solving heuristics:

- If you are having difficulty understanding a problem, try drawing a picture.
- If you can’t find a solution, try assuming that you have a solution and seeing what you can derive from that (“working backward”).
- If the problem is abstract, try examining a concrete example.
- Try solving a more general problem first. This is the “inventor’s paradox”: a more ambitious plan may actually have more chances of success.

While I never studied these heuristics, I think I use them all. I probably learned them by trial and error. Maybe we ought to teach those.

I would add a few which I feel are very potent:

- Try to sketch a solution hastily, then try to find faults in your solution.
- If you can’t solve a problem, try to solve a related, but simpler problem.
- If you can’t solve a problem, try dividing into smaller problems (divide-and-conquer).

Daniel Lemire, "Problem Solving Heuristics," in *Daniel Lemire's blog*, April 23, 2006.

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