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).