Problem A. 626. (November 2014)

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

(5 pont)

Deadline expired on December 10, 2014.

Statistics:

6 students sent a solution.
5 points:	Fehér Zsombor, Nagy-György Pál, Szabó 789 Barnabás, Wei Cong Wu, Williams Kada.
0 point:	1 student.

Problems in Mathematics of KöMaL, November 2014