Problem

Source: OLCOMA Costa Rica National Olympiad, Final Round, 2017 Shortlist LR2 day1(logical reasoning)

Tags: combinatorics, Sets



There is a set of $17$ consecutive positive integers. Let $m$ be the smallest of these numbers. Determine for which values of $m$ the set can be divided into three subsets disjoint, such that the sum of the elements of each subset is the same.