Consider the following two-player game. There are stones placed on a table. Players alternate turns. On a player's turn, they must remove k stones for some 0 In this example game, Bob loses. However, neither player played optimally! Assuming both players play optimally, provide a rule that, given n, determines whether Alice wins. Prove the correctness of this rule via mathematical induction. Hint: a move is always available except when n = 1.