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subsets of subset has same sum

Source: 2015 China TST 2 Day 2 Q2

March 19, 2015
combinatoricscombinatorics proposed

Problem Statement

Set SS to be a subset of size 6868 of {1,2,...,2015}\{1,2,...,2015\}. Prove that there exist 33 pairwise disjoint, non-empty subsets A,B,CA,B,C such that ∣A∣=∣B∣=∣C∣|A|=|B|=|C| and ∑a∈Aa=∑b∈Bb=∑c∈Cc\sum_{a\in A}a=\sum_{b\in B}b=\sum_{c\in C}c
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