n points in plane, convex heptagon and pentagon conditions
Source: Ukraine TST 2015 p9
May 2, 2020
Heptagonpentagonconvexpointscombinatoricscombinatorial geometry
Problem Statement
The set consists of points on the plane and satisfies the conditions:
there are points in the set , which are vertices of a convex heptagon,
for arbitrary five points with , which are vertices of a convex pentagon, there is a point that also belongs to and lies inside this pentagon.
Find the smallest possible value that can take .