Cover a chessboard missing two corners with dominoes — it can't be done
Take a standard 8x8 chessboard and cut off two diagonally opposite corner squares, leaving 62 squares. You have 31 dominoes, each covering exactly two adjacent squares. Can you tile the mutilated board completely?
Reveal the answer
No. Opposite corners are always the same colour, so removing both leaves 32 squares of one colour and only 30 of the other — and every domino must cover one square of each colour, so the counts can never match. Philosopher Max Black published the puzzle and its colouring proof in 1946; Martin Gardner later popularised it as a favourite example of how the right representation makes a hard-looking problem trivial.