Chomp is a game in which two players take turns choosing cells of an m × n matrix, with the rule that if a cell has been selected, then it and all cells below and/or to the right of it are removed from consideration (graphically, filled in) and cannot be selected in the remainder of the game. That is, if cell (j, k) is selected, then one fills in all cells of the form (j', k') with j' ,Ú j and k ≥ k. The player who is forced to pick the top-left corner cell [cell (1, 1)] loses; the other player wins. Player 1 moves first.

Analyze this game and determine which player has a strategy guaranteeing victory. Explain how the identity of the player with the winning strategy depends on m and n. Can you calculate the winning strategy, for at least some cases of m and n?