Prove that for any natural number m there exists a natural number n such that any n distinct points on the plane can be partitioned into m non-empty sets whose convex hulls have a common point.
The convex hull of a finite set X of points on the plane is the set of points lying inside or on the boundary of at least one convex polygon with vertices in X, including degenerate ones, that is, the segment and the point are considered convex polygons. No three vertices of a convex polygon are collinear. The polygon contains its border. combinatorial geometrycombinatoricsConvex hull