Given a collection of (not necessarily distinct) integers, how large must the collection be to guarantee that for a particular $n$, there is a subcollection of $n$ numbers summing to a multiple of $n$?
A glance shows that for any $n$, at least $2n-1$ are required, since if we have a collection of $n-1$ 0's and $n-1$ 1's, then there is no way to sum to a multiple of $n$. Is there an elegant way to prove $2n-1$ is always sufficient?