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8. A crazy clock is a clock whose numbers 1-12 are permuted. The usual clock is a crazy clock. (a) How many crazy clocks are

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8. A crazy clock is a clock whose numbers 1-12 are permuted. The usual clock is a crazy clock. (a) How many crazy clocks are there that are not the usual clock or rotations of it? (b) How many crazy clocks are there modulo rotation? (c) Prove: given a crazy clock, there exists a sequence of three adjacent numbers around the clock whose sum is at least 20

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