Problem

Source: MOP 2005 Homework - Blue Group #14

Tags: combinatorics unsolved, combinatorics



Let $S$ be a set of points in the plane satisfying the following conditions: (a) there are seven points in $S$ that form a convex heptagon; and (b) for any five points in $S$, if they form a convex pentagon, then there is point in $S$ lies in the interior of the pentagon. Determine the minimum value of the number of elements in $S$.