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partition a set of 1,2,3,.., n into 3 disjoint sets wit equal sum of elements

Source: Greece JBMO TST 2014 p4

April 29, 2019
combinatoricsset theorySetsSubsetspartitionsumsSum

Problem Statement

Givan the set S={1,2,3,....,n}S = \{1,2,3,....,n\}. We want to partition the set SS into three subsets A,B,CA,B,C disjoint (to each other) with A∪B∪C=SA\cup B\cup C=S , such that the sums of their elements SASBSCS_{A} S_{B} S_{C} to be equal .Examine if this is possible when: a) n=2014n=2014 b) n=2015n=2015 c) n=2018n=2018
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