MathDB

Consider a regular 2n-gon

P

A_1,A_2,\cdots ,A_{2n}

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, Macedonia
JBMO 2017, Q4

Problem Statement