Re: a couple entries ago, the one where I engaged in EWD worship, I mentioned a nifty proof in his essay but left it out.
It's a cool proof because: 1) it requires no knowledge of math 2) it requires no knowledge of chess 3) it makes his point about looking at a set as a whole rather than bit by bit.
To recap, say you remove the 2 squares on opposite corners of a chess board. Prove you can't cover the remaining board w/ 2x1 dominoes.
The proof: those squares will be the same color (see chessboard). So you'll have 30 white and 32 black sq. Or 32 black and 30 white. It's not important which, the important thing is there are an unequal # of black and white squares.
Every 2x1 domino will cover a black and white square. So if there's a covering, there will be exactly the same number of black and white squares covered. Only there isn't the same number of black and white squares, so you can't. QED.