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dividing a set into 2 sets with same sum each

Source: INAMO Shortlist 2015 C2

July 9, 2019
combinatoricsarithmeticSets

Problem Statement

Given 2n2n natural numbers, so that the average arithmetic of those 2n2n number is 22. If all the number is not more than 2n2n. Prove we can divide those 2n2n numbers into 22 sets, so that the sum of each set to be the same.
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