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 triom

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