1. Consider the following game: suppose there are three piles of stones starting with 3, 5, and 7 in each pile. Two players take turn playing this game. During their turn, a player can choose one of the three piles that are currently nonempty and remove any positive number of stones currently presented in that pile. \"Whoever takes the last stone loses the game. (a) [5 points) Describe how to model this game using a graph, in such a way that paths in your graph represent the dierent states that you can have in this game. Specify whether your graph is directed or undirected. Careilly describe what the vertices of your graph represent, and when two vertices are connected with an edge. (b) [3 points) Suppose Player 1 [who makes the rst move in this game) just won. What can you say about the path from [3, 5, 7) to (U, U', U) in this graph? (c) [7 points) Suppose the game currently has 1 stone in the rst pile, 2 stones in the second, and 2 stones in the third, and it is Player 1's turn to make their move. Describe a winning strategy for this player