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

In a hut in Madagascar is a camp of chameleons. Some are red, some green, some orange, in a particular ratio. As they face off, can you tell if they will ever all be the same colour?
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Updated on Oct 09, 2021 04:37 PM IST
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By By Dilip D’Souza

Wandering around Madagascar years ago, I ran across chameleons every now and then. With their large heads, bug-eyes, coiled tails, fluorescent green bodies and deliberately slow way of walking, they were photogenic and strangely gorgeous. I never caught one changing colours, though people I met — the friendly Madagascar folks — assured it me that it happens.

There was a story I heard about them. Seems a friendly young Madagascar woman once walked into an empty hut and found that it wasn’t actually empty. There were 48 chameleons running about in there — or, well, walking about in that deliberately slow way. Of these, 13 were green, 14 were orange and 21 were red. The young woman’s eyes nearly popped in wonder and she ran to call her family to come watch this chameleon conclave.

OK, I made up that story. But let’s make a puzzle of it anyway.

When two chameleons of different colours (green and orange, for example) come face to face, both change to the third colour (red, in this case). Is it possible that when the young woman returns to the hut with her family, all the chameleons will be the same colour?

Whatever your answer, explain why.

Scroll down for the answer.

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Answer:

No, they will never all be the same colour.

On any given face-to-face meeting — green and orange, say — the difference between the counts of those two colours stays the same (because each loses one). Since red increases by 2, the difference between green and red either increases or decreases by 3 — and the same for orange and red. (For example, after the first green-orange meeting, the counts go from 13 green, 14 orange and 21 red to 12 green, 13 orange and 23 red.)

So for two colours to vanish, their initial difference would have to be a multiple of 3. And that’s not the case in this hut overrun by chameleons!

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Wednesday, October 20, 2021