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On a circular array with n positions, we wish to place the integers 1, 2, ......

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Advance Math

On a circular array with n positions, we wish to place theintegers 1, 2, ... r in order, clockwise, such that consecutiveintegers, including the pair (r,1) are not in adjacent positions onthe array. Arrangements obtained by rotation are considered thesame. In how many ways can this be done? Give a combinatorialproof.

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