Question 76
Let $n \geq 2$ be a positive integer. A subset of positive integers $S$ is called comprehensive if for every integer $0 \leq x \lt n$, there is a subset of $S$ whose sum of elements has remainder $x$ when divided by $n$. Note that the empty set has sum $0$. Show that if a set $S$ is comprehensive then there is some (not necessarily proper) subset of $S$ with at most $n-1$ elements which is also comprehensive.