Combinatorics · Invariants · Modular arithmetic · Reachability · State changing process
An island is inhabited by \(45\) chameleons: \(17\) yellow, \(15\) grey and \(13\) blue. They wander about and meet from time to time, never more than two at a time. When two chameleons of the same colour meet, their colours stay as they are. When two chameleons of different colours meet, both of them change into the third colour (for instance, if a yellow and a grey chameleon meet, both turn blue).
Can it happen that from some moment on all the chameleons on the island have the same colour?
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Serbian Republic Competition (Republicko takmicenje) 2000, high school grade I, category A, problem 4. Organized by the Mathematical Society of Serbia (DMS). Source