Consider a game of Nim in which the players have some number of chips in their
pockets. A legal move is either one of the usual legal moves of Nim or involves moving some positive
number of chips from the player’s pocket on to one of the piles. (Notice that no chip is ever returned
to 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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