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4. (1.8.33) Suppose we change the object of Nim so that the player who takes the last coin loses, This is called the misere version of Nim. (a) Show that the following is a winning strategy: Play as in ordinary Nim until all but exactly one heap contains a single coin. Then remove either all or all but one of the coins of the exceptional heap so as to leave an odd number of heaps of size 1. (b) In which initial set-ups is player 1 guaranteed to win, and in which player 2