We wanted to find the minimum number of points of each colour for a set. The most important thing to notice is that if one type of point connects to another type at a different frequency than vice versa, than the ratio of their sizes is the inverse of that difference. Put simply, if red points connect to 2 orange points and each orange point connects to 1 red point, there are twice as many orange points as red points. Repeat this to find a collective ratio of 1:2:4:3:1:1. Since red points connect to 1 other red point, we can thus find our answer. There is a minimum of 2 red points, 4 orange points, 8 yellow points, 6 green points, 2 blue points, and lastly, 2 purple points.