MathNet 2014 Question 72

Let $n\ge1$ be an integer. A set of $4n+5$ points in the plane has no three collinear, and each point is red or blue. Prove that there are $n$ triangles whose vertices all have one color, the same for all triangles, whose interiors are pairwise disjoint and contain no colored point.

Illustrative case n=1: nine points, five red and four blue, with no three collinear; no triangles are selected.