BG-MO 1993 Problem 3

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.