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1. A game for two players starts with an empty pile. Players take turns putting 1 or 2 or 3 pennies in the pile. The winner is the player who brings the value of the pile up to 16 Make a directed graph modeling this game. Since this is a large graph, you may wish to a. find a way to minimize it without loss of information. b. Show that the second player has winning strategy by finding a set of four "good" pile including 16c, such that the second player can always move to one of the "good" piles (when the second player moves to one of the good piles, the next move of the first player must be to a non good pile, and from this position the second player has a move to a good pile, etc.)