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partition with same cardinality and same sum of elements of {1,2,3,...,n}

Source: Indian Postal Coaching 2008 set 6 p4

May 25, 2020

partitioncombinatoricsSubsets

Problem Statement

Consider the set

A = \{1, 2, ..., n\}

, where

n \in N, n \ge 6

. Show that

A

is the union of three pairwise disjoint sets, with the same cardinality and the same sum of their elements, if and only if

n

is a multiple of

3