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Problem of the Week 1031

Counting Combs

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Consider the set A = {1, 2, 3, ..., 1031}. In how many ways can A be partitioned into disjoint sets A = B1 ∪ B2 ∪ ... ∪ B_r such that each B_i is an arithmetic progression having 1 or more elements and common difference 2?

Source: Amer Math Monthly January, 2005.

© Copyright 2005 Stan Wagon. Reproduced with permission.

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30 March 2005