MathDB

it is given a polyhedral constructed from two regular pyramids with bases heptagons (a polygon with

7

vertices) with common base

A_1A_2A_3A_4A_5A_6A_7

and vertices respectively the points

B

and

C

. The edges

BA_i , CA_i

(i = 1,...,7

), diagonals of the common base are painted in blue or red. Prove that there exists three vertices of the polyhedral given which forms a triangle with all sizes in the same color.

Problem Statement