PROBLEM 6 Bulgarian solitaire is a game played by one player. The game starts with 6 coins distributed in 1-6 piles. Then the player repeats the following step: e Remove one coin from each existing pile and form a new pile. The order of the piles doesn't matter, so the state can be described as a sequence of positive integers in non-increasing order adding up to 6. For example, the first two moves when a player begins with two piles of 3 coins are (3,3) (2,2,2) and (2,2,2) (3,1,1,1). On the next move, the last three piles disappear, creating piles of 4 and 2 coins. (A) Trace the sequence of moves starting from two initial piles of 3 until it repeats. (B) Draw as a directed graph the complete state space with six coins. (C) Show that if the stacks are of heights n,n 1,...1 for any arbitrary number of coins n, the next configuration is the same. Solution. Write your answer here