Moldova JTST 2019 P8
Source:
April 19, 2019
combinatorics
Problem Statement
It is considered a regular polygon with sides, where is an odd number that does not divide by 3. From the vertices of the polygon are arbitrarily chosen vertices that are colored in red and the others in black. A triangle with the vertices at the vertices of the polygon it is considered ,if all of its vertices are of the same color. Prove that the number of all isosceles triangles with the vertices at the given polygon ends does not depend on the way of coloring of the vertices of the polygon. Determine the number of all these isosceles triangles.