Mutilated chessboard problem
This is a famous puzzle first seen in a Scientific American under Mathematical Games entitled "The Mutilated Chessboard" by Martin Gardner. The puzzle was stated as follows.
The props for this problem are a chessboard and 32 dominoes. Each domino is of such size that it exactly covers two adjacent squares on the board. The 32 dominoes therefore can cover all 64 of the chessboard squares. But no suppose we cut off two squares at diagonally opposite corners of the board and discard one of the dominoes. Is it possible to place the 31 dominoes on the board so that all the remaining 62 squares are covered? If so, show haw it can be done. If not, prove it impossible.
Solution
The puzzle is impossible. Each domino covers one white square and one black square. 31 dominoes would cover 31 white and 31 black squares, leaving 1 white and 1 black square uncovered. But the two covered squares were originally both white.
External Links
My Best Mathematical and Logic Puzzles By Martin. Gardner