Question 6
Let $a_1$, $a_2$, …, $a_n$ be distinct positive integers and let $M$ be a set of $n-1$ positive integers not containing $s = a_1 + \dots + a_n$. A grasshopper is to jump along the real axis, starting at the point $0$ and making $n$ jumps to the right with lengths $a_1$, $a_2$, …, $a_n$ in some order. Prove that the order can be chosen in such a way that the grasshopper never lands on any point in $M$.