[lordnacho]

It's simultaneously fascinating and frustrating when you run into a problem that suits those criteria.

In this case of course the hint is well disguised: if you had an unmarked board you might not think to checker it, but a checkered board is a common thing, so you might not think anything of it when someone presents it as part of the problem.

Reminds me of how you find the area under exp(-x^2). Stare at it for a bit and it looks like it can't be done. But if you add another dimension to it, you find the solution.

And this is what is both fascinating and frustrating. You could add a lot of things to a problem without making any progress, but there are certain things you can do that make it simple.