Problem 5 (due Monday, April 10)
Consider a set $S$ of $n$ distinct points on a plane. A circle is called minimal for S if every point of $S$ is either on the circle or inside the circle and there are at lest 3 points from $S$ on the circle. What is the largest possible number of minimal circles a set with $n$ points can have?
We did not receive any correct solutions (we received one solution which was not correct). The answer to the problem is $n-2$ for all $n\geq 3$. For a detailed solution see the following link Solution.