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(10 p) Use the minmax game strategy to play NIM. The rules for NIM are simple. Place a number of tokens between two opponents; at each move, the player whose turn comes must divide a pile of tokens into two non-empty piles of different sizes. The first player who can no longer make a move loses the game. (a) Play NIM starting with a pile of 7 (seven) tokens with the MIN player making the first move. Find the value of the game, i.e., determine the winner (MIN or MAX) for NIM when both players use the minmax strategy. Develop the whole state space for the game and show using bold face the solution path. (b)Consider the tree developed at (a). Use the left-to-right alpha-beta pruning procedure and show what nodes would not need to be examined. (c) Consider again the tree developed at (a). Use the right-to-left alpha-beta pruning procedure and show what nodes would not need to be examined (10 p) Use the minmax game strategy to play NIM. The rules for NIM are simple. Place a number of tokens between two opponents; at each move, the player whose turn comes must divide a pile of tokens into two non-empty piles of different sizes. The first player who can no longer make a move loses the game. (a) Play NIM starting with a pile of 7 (seven) tokens with the MIN player making the first move. Find the value of the game, i.e., determine the winner (MIN or MAX) for NIM when both players use the minmax strategy. Develop the whole state space for the game and show using bold face the solution path. (b)Consider the tree developed at (a). Use the left-to-right alpha-beta pruning procedure and show what nodes would not need to be examined. (c) Consider again the tree developed at (a). Use the right-to-left alpha-beta pruning procedure and show what nodes would not need to be examined