The Mutilated Chessboard
A chessboard has 64 squares, 8 by 8. If you have 32 dominoes, each the size of 2 side-by-side chessboard squares, you’ll be able to exactly cover the chessboard with the dominoes. (In fact, there are very many ways you could arrange the dominoes to cover the 64 squares of the board!)
But suppose you cut off any two diagonally opposite corner squares of the chessboard, leaving 62 squares. What patterns of 31 dominoes will exactly cover the mutilated chessboard?
This is another good exercise in creative problem-solving. Try to observe your own thought processes as you try to solve this. Are you methodical or do you make random guesses? Do you visualize solving the problem or analyze it differently? Do you attack the whole problem head-on, or try to solve a similar but smaller and simpler problem first?