Question 32
Monica and Bogdan are playing a game that depends on two positive integers $n$ and $k$. First, Monica chooses and writes $k$ positive numbers. Bogdan wins if he manages to mark $n$ points on the plane so that for each number $m$ written by Monica, there are two marked points at a distance precisely $m$, otherwise Monica wins. Find out, depending on $n$ and $k$, who wins, if both players play optimally.
(Fedir Yudin)
(Fedir Yudin)