http://cotpi.com/p/17/ (I first got this puzzle from Prunthaban.)
There are 64 pawns placed on a chessboard. Each square contains a
pawn. Two players are on the same side of the chessboard. Each player
takes turns and removes a pawn along with all pawns above it and to
its right. The player who picks the pawn at the bottom-left corner
loses. Who can definitely win the game?