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Forall chameleons to become of the same color, the number of chameleons of any two colors must become the same. (Then they all meet, and turn into chameleons of the third color.)
In other words, the difference between chameleon populations must become 0.
Initially, this difference is 2 between red and green, 2 between green and blue and 4 between red and blue.
Whenever two different color chameleons meet, they become the third color. That means that if chameleon ofcolor A meets one of color B, they turn to color C. Thus the populations for A and B have gone down by 1 each, and the population of C has gone up two. Therefore, the difference between A and C, and B and C has been changed by 3. (The difference between A and B is obviously unchanged.)
Since there is no amount of adding or subtracting 3 that can turn either 2 or 4 into 0, there is no way for the population to ever become the same color. |
