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Unformatted text preview: ( a +1) mice of which one is descended from the preceding, or there are ( b +1) mice of which non descends from the other. Problem 5. Thirtythree rooks are placed on an 8 × 8 chessboard. Prove that you can choose ±ve of them which are not attacking each other. Problem 6. Let a , a 1 , · · · , a 100 and b , b 1 , · · · , b 100 be two permutations of the integers from 1 to 100. Prove that, among the products a 1 b 1 , · · · , a 100 b 100 , there are two with the same remainder upon division by 100. 1...
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 Spring '11
 Dolatabadi

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