It is known (see [this other answer](http://mathoverflow.net/a/9381)) that an 8x8 board in which squares at opposite corners have been removed cannot be tiled with dominoes, as the removed squares are of the same "colour". But what if two squares of *different* colours are removed? Ralph E. Gomory showed that it is always possible, no matter where the two removed squares are, and this is his proof:

![Image of board][2]


(Imagine A and B are the squares removed.) The image is from _Mathematical Gems I_ by Ross Honsberger.


  [2]: https://i.sstatic.net/Yh9nT.png