Given 30 points in the plane no 3 of which are collinear, we color the segments formed by the pairs of these points red and blue such that: from every point there emerge 12 red segments and 17 blue segments. How many triangles that have all three sides of the same colour are there?
N.B. i think the phrasing of the problem is bad - the number of monochromatic triangles surely cannot be constant right? However it’s rather hard for me to construct two examples with a different number of triangles. Maybe the problem wanted the minimum number of such triangles