Donald and Kim plays the following game. There is a jar containing 100 stones. The two players (D and K) take turns. When it is a player's turn to move, he must take between 1 and 10 stones from the jar, so there are potentially 11 different options at each move (depending on how many stones are left in the vase at that point). The game ends when the jar is empty and the player who emptied the jar wins the game. D generously offers to let K move first.

1. If there is common knowledge of rationality and the rules of the game, so that both players will move optimally at all their decision nodes in the game, who will win the game? Use backwards induction and explain your reasoning.

2. Describe the full backwards induction solution strategies in the game. A full strategy must include an action at any decision node the game could possibly reach.