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One taken from each of any n − 1 of the subsets

Source: IMO Shortlist 1995, N7

August 10, 2008
combinatoricspartitionAdditive combinatoricsAdditive Number TheoryIMO Shortlist

Problem Statement

Does there exist an integer n>1 n > 1 which satisfies the following condition? The set of positive integers can be partitioned into n n nonempty subsets, such that an arbitrary sum of n \minus{} 1 integers, one taken from each of any n \minus{} 1 of the subsets, lies in the remaining subset.
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