Any meeting of chameleons (of different colour) leads to a change in their numbers like this: -1/-1/+2. Thus, during any such meeting, the difference in numbers of any two species changes by three, or not at all. Now, imagine the penultimate step, just before all chameleons turn into the same colour: there must be two species with one specimen each. Therefore, we have to get to a point where the difference in population between two of the three species is zero. But this cannot be, as we start out with differences of two and four, and we can only change them in steps of three.

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