The following problem, devised by Ginger Bolton, appeared in the January 1989 issue of the College Mathematics Journal (Vol. 20, No. 1, p. 68): Given a positive integer n ≥ 2, let S be the set of all nonempty subsets of {2, 3, …, n}. For each Si ∈ S, let Pi be the product of the elements of Si. Prove or disprove that

 

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24-1 E P. = (n + 1)! 1. 2 24-1 E P. = (n + 1)! 1. 2