color the vertices of a regular $2005-$ gon
Source: Croatian NMC 2005, 3rd Grade
May 8, 2007
combinatorics proposedcombinatorics
Problem Statement
The vertices of a regular -gon are colored red, white and blue. Whenever two vertices of different colors stand next to each other, we are allowed to recolor them into the third color.
(a) Prove that there exists a finite sequence of allowed recolorings after which all the vertices are of the same color.
(b) Is that color uniquely determined by the initial coloring?