Sunday, 16 September 2012

Dominoes on a square board

Suppose you have cut off the two diagonally opposite corner squares of a regular 8×8 square board, as shown above, 62 squares remain. Now you have a set of 2×1 dominoes, each of which covers two squares that are adjacent vertically or horizontally. Is it possible to use 31 of these dominoes to tile all 62 squares?

1 comment:

  1. No. Picture the 8x8 board as a chess board. Then two diagonally opposite squares would be of the same color . Now, we have 30 black and 32 white squares. Each domino would have to cover precisely 1 white and 1 black which would make allow filling only 60 squares. i.e., maximum 30 dominoes.