Balanced line for a 3-colored point set in the plane (Q426795)

Summary: In this note we prove the following theorem. For any three sets of points in the plane, each of \(n\geq 2\) points such that any three points (from the union of three sets) are not collinear and the convex hull of \(3n\) points is monochromatic, there exists an integer \(k\in\{1,2,\dots,n-1\}\) and an open half-plane containing exactly \(k\) points from each set.