Kermit and Fozzie play a game with two jars, each containing 100 pennies. The players take turns, Kermit goes first. Each time it is a player's turn, he chooses one of the jars and removes anywhere from 1 to 10 pennies from it. The player whose move leaves both jars empty wins(Note that when a player empties the second jar, the first jar must already have been emptied in some previous move by one of the players.)
a) Does this game have a first-move advantage or a second-mover advantage? Explain which player can guarantee victory, and how he can do it.(Hint: Simplify the game by starting with a smaller number of pennies in each jar, and see, if you can generalize your finding to the actual game.)
b) What are the optimal strategies (complete plans of action) for each player? (Hint: First think of a starting situation in which both jars have equal numbers of pennies. Then consider starting positions in which the two jars differ by 1 to 10 pennies. Finally, consider starting positions in which the jars differ by more than 10 pennies.)