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Part of 2012 Switzerland - Final Round

Problems(1)

2012 chameleons sitting at a round table, red or green

Source: Switzerland - 2012 Swiss MO Final Round p1

12/30/2022
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 20122012 minutes there are at least 22 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.
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