Consider a regular 2n-gon P,A1,A2,⋯,A2n 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 color the sides of P in 3 different colors (ignore the vertices of P,we consider them colorless), such that every side is colored in exactly one color, and each color is used at least once . Moreover ,from every point in the plane external to P , points of most 2 different colors on P can be seen .Find the number of distinct such colorings of P (two colorings are considered distinct if at least one of sides is colored differently).Proposed by Viktor Simjanoski, MacedoniaJBMO 2017, Q4 combinatorial geometrycombinatorics