[math-fun] Largest sum-free subset of {0,1,2,...,2n}

Prove that if S is a subset of {0,1,2,...,2n} containing more than n elements, then there must exist x,y,z in S such that x+y=z. (This smells like an Olympiad problem to me. In fact, I may well have solved this very problem forty years ago, but I don't see how to solve it now. Some sort of pigeonhole argument, sure, but how to set it up?) The bound is tight; both 1,3,5,...,2n-1 and n+1,...,2n are sum-free. Jim Propp