OK, this is not really a chess problem, so I'll put it here...
Imagine a chessboard, but with the two corner white squares cut out.
You have 31 identical dominoes, each shaped to cover precisely 2 chess squares, horizontally or vertically (but, naturally, not diagonally).
Can you arrange the dominoes to cover the altered board completely? If so, how? If not, why not?
Prize of a game against me (
) for the most elegant solution, which doesn't involve "I tried it every way I could think, and I can't do it"