This game is called Chomp. It is normally played with just a table of squares on a piece of paper between two players, but I find it easier to understand by thinking of a chocolate bar like this:
My favorite Chomp playing board
To understand how to play the game, click here to go to UCLA and play against their computer. It can be proven mathematically that the first player can always win, but the proof doesn't show how to do it. See if you can win at UCLA and come back and tell us how you did it.
Warning: This game is not really a game, but rather a unsolved proof that mathematicians have been trying to solve for quite a while. It is HARD. Do not spend too much time on it.
Credits: The game was originally stated by Fred Schuh in 1952 as his "game of divisors". David Gale reinvented this game. His version used an m-by-n (any size rectangular) chocolate bar. The name Chomp was invented by Martin Gardner in Scientific American.