2017 JBMO Problems/Problem 4
Consider a regular 2n-gon , in the plane ,where is a positive integer . We say that a point on one of the sides of can be seen from a point that is external to , if the line segment contains no other points that lie on the sides of except .We color the sides of in 3 different colors (ignore the vertices of ,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 , points of most 2 different colors on can be seen .Find the number of distinct such colorings of (two colorings are considered distinct if at least one of sides is colored differently).
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