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Putnam 1973 B1

Source: Putnam 1973

May 29, 2022
PutnamIntegers

Problem Statement

Let a1,a2,…a2n+1a_1, a_2, \ldots a_{2n+1} be a set of integers such that, if any one of them is removed, the remaining ones can be divided into two sets of nn integers with equal sums. Prove a1=a2=⋯=a2n+1.a_{1}=a_2 =\cdots=a_{2n+1}.
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