MathNet 2010 — Part 01 Question 120

Fifteen points are marked on a plane. Some of them are painted red, some others are painted blue, and all remained points are painted green. It is known that the number of the red points is the largest. The sum of the distances between the red points and the blue points is $5$, the sum of the distances between the red points and the green points is $31$, and the sum of the distances between the blue points and the green points is $25$.
Find the number of points of each color.
(I. Voronovich)