n points on plane partitioned into m sets whose convex hulls have common point
Source: SRMC 2020 P4 - Silk Road
August 18, 2020
combinatorial geometrycombinatoricsConvex hull
Problem Statement
Prove that for any natural number there exists a natural number such that any distinct points on the plane can be partitioned into non-empty sets whose convex hulls have a common point.
The convex hull of a finite set 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 , 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.