Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# 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