A. 626. We have \(\displaystyle 4n+5\) points on the plane, no three of them are collinear. The points are colored with two colors. Prove that from the points we can form \(\displaystyle n\) empty triangles (they have no colored points in their interiors) with pairwise disjoint interiors such that all points occurring as vertices of the \(\displaystyle n\) triangles have the same color.
Miklós Schweitzer competition, 2014
Deadline expired on 10 December 2014.