Consider a game with two teams and m 1000 + 1 flags. The two teams alternate moves, with Team 1 moving first. When it's a team's turn to move must remove j flags, where j {1, 2, . . . , m 1}, where m 1 > 1. The team that takes the last flag wins.

(a) Does one of the teams have a winning strategy? If so, describe it.

(b) Suppose that the team that takes the last flag loses. In this case, does one of the teams have a winning strategy? If so describe it.