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Unformatted text preview: (4) 1994 girls are seated around a table. Initially, one girl has n tokens. Each turn, some girl with at least two tokens passes one token to each of her neighbors. The game ends when every girl has at most one token. Show that if n < 1994, the game must terminate, while if n = 1994, the game cannot terminate. (5) A game starts with four heaps of beans, containing 3 , 4 , 5 and 6 beans. Two players move alternately. A move consists of taking either (a) one bean from a heap, provided at least two beans are left behind in that heap, or (b) a complete heap of two or three beans. The player who takes the last heap wins. To win the game, do you want to move rst or second? Give a winning strategy. 1...
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 Fall '09

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