Answer to Puzzle #16: Covering a Chess Board With Dominoes

16. You have a chessboard (8x8) plus a big box of dominoes (each 2x1). I use a marker pen to put an "X" in the squares at coordinates (1, 1) and (8, 8) - a pair of diagonally opposing corners. Is it possible to cover the remaining 62 squares using the dominoes without any of them sticking out over the edge of the board and without any of them overlapping? You cannot let the dominoes stand on their ends

Easy when you know how....

Before reading the answer can I interest you in a clue?

The nature of this problem is such that if you can't find a hook you'll be thinking about it for ever.

Firstly the answer to this question is NO you can't cover the board. There is a trick here, look at the board below.

picture of a chessboard

Do you notice anything about the squares at 1,1 and 8,8? Well they are both the same colour.

If you think about a Domino placed anywhere on the board it will necessarily cover a black square and a white square. We have in our example a 32 black squares and 30 white squares to cover. So it just can't be done.





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