Covering Solution

Alright, I'm pretty sure I still have this blog, and now I have something of a backlog of puzzles to post. Something of an embarrassment of riches that I don't bother to post as often as I learn new puzzles, but thats life I guess. Anyway, time for the solution to the domino problem from last time.

The solution is very simple: Consider naming the squares on the chessboard black and white, with no two of the same colour adjacent (the way chessboards are actually coloured). A given domino must cover exactly 1 white and 1 black square. The standard chessboard has 32 squares of each colour, but opposite corners are always the same colour so removing two of opposite corners will leave us with 32 squares of one colour and 30 of the other. It will not be possible to cover this with 31 dominoes.

Thats it really, I'll follow this with a post about the follow up problem.