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2 disjoint subsets of {1,2, ... ,m} with same sums of elements, max cardinal

Source: Mexican Mathematical Olympiad 1988 OMM P7

July 27, 2018
combinatoricsSumSubsets

Problem Statement

Two disjoint subsets of the set {1,2,...,m}\{1,2, ... ,m\} have the same sums of elements. Prove that each of the subsets A,BA,B has less than m/2m / \sqrt2 elements.
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