A game of Nim

(Pocket Nim)  Consider a game of Nim in which the players have some number of chips in theirpockets. A legal move is either one of the usual legal moves of Nim, or involves moving some positivenumber of chips from the player’s pocket on to one of the piles. (Notice that no chip is ever returnedto a pocket.)(a) Show that the game is progressively bounded.(b) Find the sets N  and P .(c) Describe the winning strategy.

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