Prove that there exists a function $f: \mathbb{N} \to \mathbb{N}$ such that a partitioning of $\{1,2,...,f(n)\}$ into $n$ classes will have some $x,y$ such that $x$, $y$ and $x+y$ all belong to the same class.
I'm very stuck on this... I imagine the answer is something to with Stirling numbers of the second kind but I'm really struggling to achieve any more than this! All I've deduced is the bound that $f(n)>n$ which is pretty trivial really...