2. Consider the following two person parlor game, which starts with n counters on the table in front of the two players. Players 1 and 2 move sequentially, player 1 moving first. When it is his turn to move, a player must remove either 1 or 2 counters from the table. The game ends when all the counters are removed, and the player who moves last wins the game. a) Suppose that n = 15. Solve the game by backwards induction. (Hint: let & be the number of counters left on the table. Focus on the winning positions - the value of k where a player wins - and losing positions for a player. Start with small values of k, i..e '* = 1 and k = 2. ) b) How would you generalize your answer in (a), so that for any n, you can determine which player wins the game in the backwards induction solution