Question 2
Let $n,m$ be positive integers such that $n\ge2m+1$. Given $n$ distinct points and $nm$ distinct line segments, each joining a pair of points, prove that there exist distinct points $A_0,A_1,\ldots,A_m$, so that for each $i=0,\ldots,m-1$, there is a line segment joining $A_i$ to $A_{i+1}$.