(Pocket Nim) Consider a game of Nim in which the players have some number of chips in their pockets.

(Pocket Nim)  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.