Fifth Question I Nim (Grundy) is a two-player game. The rules are as follows. The game starts with a single stack of 8 tokens. At each move a player selects one stack and divides it into two non-empty, non-equal stacks. A player who is unable to move loses the game. (a) Draw the complete search tree for nim. (b) Assume two players, min and max, play nim (as described above). Min plays first. If a terminal state in the search tree developed above is a win for min, a utility function of zero is assigned to that state. A utility function of 1 is assigned to a state if max wins the game. Apply the minimax algorithm to the search tree to assign utility functions to all states in the search tree. (c) If both min and max play a perfect game, who will win? Explain your answer and show the path taken by the player that wins