Wednesday, April 25, 2007
Dominoes on a chessboard puzzle
The mutilated chessboard problem is a famous puzzle introduced by Martin Gardner in his Scientific American column Mathematical Games. The problem is as follows: Suppose a standard 8x8 chessboard has two opposite corners removed, leaving 62 squares. Is it possible to place 31 dominoes of size 2x1 so as to cover all of these squares?
Solution: The puzzle is impossible. Any way you would place a domino would cover one white square and one black square. A group of 31 dominoes would cover 31 white and 31 black squares of a chessboard, leaving one white and one black square uncovered. The directions had you remove opposite corner squares, and such squares are always either both black or both white.
References: McCarthy, John (1999). "Creative Solutions to Problems". AISB Workshop on Artificial Intelligence and Creativity. Retrieved on 2007-04-27. See also: Domino tiling, My Best Mathematical and Logic Puzzles By Martin. Gardner, Dominoes on a Checker Board by Jim Loy,
Dominoes on a Checker Board. This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Dominoes on a chessboard puzzle". Link may die if entry is finally removed or merged.