The Impossible Chessboard Tiling Puzzle

If you cut two opposite corners off a chessboard, it is mathematically impossible to cover the remaining squares with dominoes. Despite having 62 squares left, no arrangement will ever work.

This puzzle works because a standard board has an equal number of black and white squares. Removing opposite corners takes away two squares of the same color, leaving you with 30 of one color and 32 of the other. Since every domino must cover exactly one black square and one white square, you will always have two leftovers. It is a brilliant example of how simple color patterns reveal hidden logic.