Problem

Source: China Northern MO 2015 grade 10 p4 CNMO

Tags: number theory, combinatorics



If the set $S = \{1,2,3,…,16\}$ is partitioned into $n$ subsets, there must be a subset in which elements $a, b, c$ (can be the same) exist, satisfying $a+ b=c$. Find the maximum value of $n$.