2012 chameleons sitting at a round table, red or green
Source: Switzerland - 2012 Swiss MO Final Round p1
December 30, 2022
combinatoricsColoring
Problem Statement
There are 2012 chameleons sitting at a round table. At the beginning each has the color red or green. After every full minute, each chamaleon, which has two neighbors of the same color, changes its color from red to green or from green to red. All others keep their color. Show that after minutes there are at least chameleons that have the same often changed color.[hide=original wording]Es sitzen 2012 Chamaleons an einem runden Tisch. Am Anfang besitzt jedes die Farbe rot oder grun. Nach jeder vollen Minute wechselt jedes Cham aleon, welches zwei gleichfarbige Nachbarn hat, seine Farbe von rot zu grun respektive von gr un zu rot. Alle anderen behalten ihre Farbe. Zeige, dass es nach 2012 Minuten mindestens 2 Chamaleons gibt, welche gleich oft die Farbe gewechselt haben.