[eli173]

I was shown a similar problem (I believe it was originally a Putnam question) which asked if you could cover a chessboard missing one corner with L-shaped triominos, and then asked to prove whether or not you could always cover a 2nx2n board with one corner missing. Neat problem

[wolfgke]

Indeed (spoiler!) an easy, but nice induction proof, which easily can be turned into an algorithm.