This puzzle was given to me by a friend of mine, who in turn heard it from someone else who neglected to provide the answer. The text of the puzzle as it was given to my friend is below:
Angels and Demons is a game I’ve made up. It’s played on an enormous chessboard, 100 squares by 100 squares. There are two pieces, the angel and the demon. The angel starts in the bottom right hand corner of the board, while the demon starts in the top left hand corner. The demon moves exactly like the king in chess. The angel moves the same way, except he must go two squares in any direction. He can’t change direction mid-move.
Capturing works in the same way as chess. The demon wins if he can capture the angel. The angel wins if he can devise a strategy to avoid the demon forever. If both players are playing perfectly, who will win the game?
Now my thinking is that the Demon will always win, regardless of the size of the chessboard. The way I look at it, if the board was 3x3 then the solution would be trivial. Similarly, if the board was 4x4, the Angel's two move advantage wouldn't help him. As soon as the Demon manages to get the Angel to the edge of the board, his two move advantage is effectively nullified, and from there it's only a matter of time until the Demon wins.
My friend, on the other hand, believes that the Angel will always be able to avoid the Demon. Unfortunately, neither of us can prove our answers mathematically. Is there a way to prove which piece would win?