MathDB
ASU 143 All Soviet Union MO 1970 coloring vertices

Source:

June 24, 2019
combinatoricscombinatorial geometryColoring

Problem Statement

The vertices of the regular nn-gon are marked with some colours (each vertex -- with one colour) in such a way, that the vertices of one colour represent the right polygon. Prove that there are two equal ones among the smaller polygons.