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Chameleon Color Change

Hard · Game Theory & Logic · Quant Trader interview question · invariant, game-theory, modulo

There is an island with 13 red chameleons, 15 green chameleons, and 17 blue chameleons. When two chameleons of different colors meet, they both change to the third color. For example, if a red and a green chameleon meet, they both become blue. Is it possible for all the chameleons to eventually become the same color?