I have no idea what this question is asking or how to prove it mathematically. I realize based on the strategy stealing theory that if player two has a winning stratagy then player one can use the same strategy by going first and since both players can't win, player one wins. How can I show this mathematically?
The game of Chomp is played by two players. In this game, cookies are laid out on a rectangular grid. The cookie in the top left position is poisoned. The two players take turns making moves; at each move, a player is required to eat a remaining cookie, together with all cookies to the right and/or below (that is all the remaining cookies in the rectangle, in which the first cookie eaten is the top left corner). The loser is the player who has no choice but to eat the poisoned cookie. Prove that if the board is square (and bigger than 1 × 1) then the first player has a winning strategy.