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Can they reach the match point? The Wknd puzzle by Dilip D’Souza

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While walking in Madagascar years ago, I came across chameleons from time to time. With their large heads, insect eyes, curled tails, fluorescent green bodies, and deliberately slow walking, they were photogenic and eerily gorgeous. I have never seen it change color, although the people I have met – the friendly people of Madagascar – have assured me that it does happen.

I heard a story about them. It appears that a sympathetic young Madagascan woman once entered an empty hut and discovered that it was not really empty. There were 48 chameleons running around in there – or, well, walking in this deliberately slow way. Of these, 13 were green, 14 were orange and 21 were red. The young woman’s eyes almost burst with wonder and she ran to call her family to come and attend this chameleon conclave.

OK, I made up this story. But let’s do a puzzle anyway.

When two chameleons of different colors (green and orange, for example) come face to face, both switch to the third color (red, in this case). Is it possible that when the young woman returns to the cabin with her family, all the chameleons are the same color?

Whatever your answer, explain why.

Scroll down for the answer.

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Reply:

No, they will never be all the same color.

In a given face-to-face meeting – green and orange, say – the difference between the number of these two colors remains the same (because each loses one). Since red increases by 2, the difference between green and red increases or decreases by 3 – and so do orange and red. (For example, after the first green-orange encounter, the counts go from 13 greens, 14 oranges, and 21 reds to 12 greens, 13 oranges, and 23 reds.)

So for two colors to disappear, their initial difference would have to be a multiple of 3. And this is not the case in this cabin invaded by chameleons!

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