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divide n packages with weights 1, 2, 3, 4, n into 3 groups of equal weight

Source: Austria Beginners' Competition 2012 p2

December 26, 2021
combinatoricsweights

Problem Statement

A postman wants to divide nn packages with weights 1,2,3,4,n1, 2, 3, 4, n into three groups of exactly the same weight. Can he do this if (a) n=2011n = 2011 ? (b) n=2012n = 2012 ?
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