|
Well, as usual, I was about to type in my proof (which I thought was elegant, considering) and my boss comes by to check up on me. We have a good relationship so I show him the problem and give him my proof, but then he thinks about it... and comes up with a better proof! I can't tell you how often this has happend...
Colour the defective chessboard with a chess colouring (one of two colours, no square has the same colour as it's adjacent square). If the shape is tiled with dominoes, then there must be an equal number of black and white squares on the board. However, because the width of the chessboard is odd, two squares of the same colour have been removed. Therefore, the board cannot be tiled with dominoes.
QED
|