Question 35
Let $n \geq 2$ be an integer. Determine the smallest positive integer $m$ such that the following holds: given $n$ points in the plane, no three on a line, one can find $m$ lines such that none of the lines passes through any of the given points and such that for every pair of given points $X \neq Y$ there is a line with $X$ and $Y$ on opposite sides of it.