Any help is appreciated for these questions. Due on 10/30.

2. Consider a game in which two players, Adam and Ben, take turns removing matchsticks from a pile. They start with 8 matchsticks, and Adam goes rst. On each turn, each player may remove either 1 or 2 matchsticks. The player who gets to remove the last matchstick wins the game. (a) (5 points) Suppose there are only 4 matchsticks left, and it is Adam's turn. How many matchsticks should Adam remove to guarantee himself a victory? Clearly EXPLAIN YOUR REASONING (it's NOT necessary for you to construct a game tree). (b) (5 points) Suppose there are only 5 matchsticks left, and it is Adam's turn. How many matchsticks should Adam remove to guarantee himself a victory? Clearly EXPLAIN YOUR REASONING (it's NOT necessary for you to construct a game tree). (c) (5 points) Now let's start from the beginning of the game. How many matchsticks should Adam remove to guarantee himself a victory? Clearly EXPLAIN YOUR REASONING (it's NOT necessary for you to construct a game tree)