Each vertex of a right $n$-gon $(n\geq 3)$ 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 $n$ can we get from an arbitrary coloring of the $n$-gon a monochromatic one (in one color)?
Problem
Source: I International Festival of Young Mathematicians Sozopol 2010, Theme for 10-12 grade
Tags: combinatorics, polygon, Coloring