Suppose that in a variation of the game of nim we allow a player to either remove one or more stones from a pile or merge the stones from two piles into one pile as long as at least one stone remains. Draw the game tree for this variation of nim if the starting position consists of three piles containing two. two, and one stone, respectively. Find the values of each vertex in the game tree and determine the winner if both players follow an optimal strategy. | Numerade

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