IN-TST 2003 Problem 9

Let $n$ be a positive integer and $\{A,B,C\}$ a partition of $\{1,2,\ldots,3n\}$ such that $|A|=|B|=|C|=n$ . Prove that there exist $x \in A$ , $y \in B$ , $z \in C$ such that one of $x,y,z$ is the sum of the other two.