The set M consists of n points on the plane and satisfies the conditions:
∙ there are 7 points in the set M, which are vertices of a convex heptagon,
∙ for arbitrary five points with M, which are vertices of a convex pentagon, there is a point that also belongs to M and lies inside this pentagon.
Find the smallest possible value that n can take . Heptagonpentagonconvexpointscombinatoricscombinatorial geometry