Let $F=\{1,2,...,100\}$ and let $G$ be any $10$-element subset of $F$. Prove that there exist two disjoint nonempty subsets $S$ and $T$ of $G$ with the same sum of elements.
Problem
Source: Greece National Olympiad 2000 , tst , Problem 1.
Tags: pigeonhole principle, combinatorics proposed, combinatorics