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Easy algebra for 8-graders

Source: Kyiv City MO 2023 8.2

May 14, 2023
algebra

Problem Statement

Positive integers kk and nn are given such that 3≤k≤n3 \le k \le n.Prove that among any nn pairwise distinct real numbers one can choose either kk numbers with positive sum, or k−1k-1 numbers with negative sum. Proposed by Mykhailo Shtandenko
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