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MathNet 2020 — Math Olympiad Vault — Part 03 Question 115

Math Olympiad Vault · MathNet 2020 — Math Olympiad Vault — Part 03

Question 115

$4 n$ coins of weights $1, 2, 3, \ldots, 4 n$ are given. Each coin is colored in one of $n$ colors and there are four coins of each color. Show that all these coins can be partitioned into two sets with the same total weight, such that each set contains two coins of each color.
(Hungary)