[lqr]

(assuming math-ish problems) Try to solve a simpler version of the problem. Keep making simplifying assumptions until you get something you can handle.

Often you realize that some parts of the original problem statement were adding complexity with no real benefit. And the techniques you use for the simple version are likely still relevant for the big version.

If the simplified version is still hopelessly difficult, it might be a good starting point for a counterexample/lower bound to convince yourself that the full problem is hard.

[Paul-Craft]

The inverse of this strategy also works well sometimes: try to solve a more general (i.e. "harder") version of the problem. Examples:

* https://math.stackexchange.com/questions/899109/problems-tha...

* https://mathoverflow.net/questions/21214/particular-problem-...

The second link has the neat particular example of showing that something is nonzero by showing that it is odd, which I quite like.

[lqr]

Agreed!