[tromp]

I like this closely related and slightly more subtle problem:

Which unique square (up to symmetry) must be left if you cover the 64 squares of a chess board with 21 3x1 trominoes?

[CrazyStat]

Knowing that the solution is unique makes this trivial to solve in a couple minutes just by scribbling on a piece of paper (I just did). It does not seem more subtle than the original.

Proving that the solution is unique may be more subtle.