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Sum

Source: Canada 2000

March 4, 2006
combinatorics unsolvedcombinatorics

Problem Statement

Let A=(a1,a2,⋯ ,a2000)A = (a_1, a_2, \cdots ,a_{2000}) be a sequence of integers each lying in the interval [−1000,1000][-1000,1000]. Suppose that the entries in A sum to 11. Show that some nonempty subsequence of AA sums to zero.
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