Problem

Source: 2018 Argentina OMA Finals L3 p5

Tags: combinatorics, combinatorial geometry, Coloring



In the plane you have $2018$ points between which there are not three on the same line. These points are colored with $30$ colors so that no two colors have the same number of points. All triangles are formed with their three vertices of different colors. Determine the number of points for each of the $30$ colors so that the total number of triangles with the three vertices of different colors is as large as possible.