The question is this:
Given $n$ integers, $(a_1, \dotsc, a_n)$, show that there is some subset $B\subseteq \{1,\dotsc, n\}$, such that $$\sum_{i\in B}i \equiv 0 \bmod n.$$
It looks likes this should be an application of the pigeon hole principle, but I'm struggling to see how to apply it.
Thanks.
Hint: Consider the numbers $$a_1,\quad a_1+a_2,\quad a_1+a_2+a_3,\dots, a_1+a_2+\cdots+a_n.$$ If one of these is divisible by $n$, we are finished. If none is divisible by $n$, there are among these no more than $n-1$ distinct remainders on division by $n$.
So by the Pigeonhole Principle, there must be two with the same remainder. Use this to reach the desired conclusion.