Consider a regular 2n+1-gon P in the plane, where n is a positive integer. We say that a point S on one of the sides of P can be seen from a point E that is external to P, if the line segment SE contains no other points that lie on the sides of P except S. We want to color the sides of P in 3 colors, such that every side is colored in exactly one color, and each color must be used at least once. Moreover, from every point in the plane external to P, at most 2 different colors on P can be seen (ignore the vertices of P, we consider them colorless). Find the largest positive integer for which such a coloring is possible. combinatoricsregular polygonColoring