Coloring beads
Source: St Petersburg Olympiad 2018, Grade 9, P4
July 13, 2018
combinatorics
Problem Statement
On the round necklace there are beads, each painted in red or blue. If a bead has adjacent beads painted the same color, it can be repainted (from red to blue or from blue to red). For what for any initial coloring of beads it is possible to make a necklace in which all beads are painted equally?