Two players, Amy and Beth, take turns choosing numbers; Amy goes first. On her turn, a player may choose any number between 1 and 10, inclusive, and this number is added to a running total. When the running total of both play ers' choices reaches 100, the game ends. Consider two alternative endings: (i) the player whose choice of number takes the total to exactly 100 is the win ner and (ii) the player whose choice of number causes this total to equal or exceed 100 is the loser. For each case, answer the following questions:
(a) Who will win the game?
(b) What are the optimal strategies (complete plans of action) for each player?