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Problem 5 of Third round - Getting a monochromatic coloring of an n-gon

Source: I International Festival of Young Mathematicians Sozopol 2010, Theme for 10-12 grade

December 14, 2019
combinatoricspolygonColoring

Problem Statement

Each vertex of a right nn-gon (n≥3)(n\geq 3) is colored in yellow, blue or red. On each turn are chosen two adjacent vertices in different color and then are recolored in the third. For which nn can we get from an arbitrary coloring of the nn-gon a monochromatic one (in one color)?
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