Two Games, One Puzzle

Arlene Blackman Yolles ♦ February 21, 2013 ♦ 5 Comments

I love the type of puzzle that is simple to explain and understand. No frills, no complicated facts, nothing hidden. Such is this puzzle that I hope you find intriguing.

Picture a checkerboard, or better yet, go get one. You know, 64 squares, alternating in color, usually black and white. Now get some dominoes or, lacking them, cut out a few paper rectangles where each covers two of the checkerboard’s squares. Here’s the question:

Can you cover the checkerboard with 31 dominoes (each covering two squares) so that the top right and bottom left squares remain uncovered? Simple yet challenging. Scroll down for the answer.

On first thought, it might seem as though it were possible. 31 dominoes cover 62 squares, leaving the 2 noted uncovered. But, think again. Originally there are 32 black and 32 white squares. Removing the top right and bottom left white squares leaves 32 black and 30 white. Each domino covers 1 black and 1 white square. After 30 dominoes are placed, 30 black and 30 white squares are covered. That leaves 2 black squares uncovered, which cannot both be covered by the same domino.  So, the correct answer is NO!