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Combinatorial geometry

Source: All-Russian Mathematical Olympiad 1994

April 9, 2009
geometrysearchcombinatorics unsolvedcombinatorics

Problem Statement

In a regular 6n\plus{}1-gon, k k vertices are painted in red and the others in blue. Prove that the number of isosceles triangles whose vertices are of the same color does not depend on the arrangement of the red vertices.