There is a finite set of points in the plane, where each point is painted in any of $ n $ different colors $ (n \ge 4) $. It is known that there is at least one point of each color and that the distance between any pair of different colored points is less than or equal a 1. Prove that it is possible to choose 3 colors so that, by removing all points of those colors, the remaining set of points can be covered with a radius circle $ \frac {1} {\sqrt {3}} $.