Problem

Source: Chinese MO 2004

Tags: combinatorics proposed, combinatorics



Let $M$ be a set consisting of $n$ points in the plane, satisfying: i) there exist $7$ points in $M$ which constitute the vertices of a convex heptagon; ii) if for any $5$ points in $M$ which constitute the vertices of a convex pentagon, then there is a point in $M$ which lies in the interior of the pentagon. Find the minimum value of $n$. Leng Gangsong