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Topic: Chameleon island (Read 2898 times) |
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BNC
Uberpuzzler
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Chameleon island
« on: Mar 30th, 2003, 1:17pm » |
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On a remote island live chameleons in 3 colors: blue, red, and green. At a certain time, there are 13 blue chameleons, 15 red, and 17 green. No chameleon ever dies, and non born (or migrate in /out of the island).
Every time two chameleons of different colors meet, they change colors to the third one (e.g., if a red chameleon meets a blue chameleon, both turn green).
Is it possible for all chameleons to turn to the same color?
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How about supercalifragilisticexpialidociouspuzzler [Towr, 2007]
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Icarus
wu::riddles Moderator
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Re: Chameleon island
« Reply #1 on: Mar 30th, 2003, 8:20pm » |
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The answer is "no". Why? Because the answer to problems stated like this one is always "no". If it were possible, the problem would be stated differently! 
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BNC
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Re: Chameleon island
« Reply #2 on: Mar 30th, 2003, 11:19pm » |
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You should know by now not to trust the way I word the riddles, hey?  
OK, add a last line:
If possible, show the shortest "path". If not, explain.
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LZJ
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Re: Chameleon island
« Reply #3 on: Mar 30th, 2003, 11:21pm » |
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It's not possible. Very briefly, one has to get either 2 of the colours to have the same number of chameleons, or with the difference in number between 2 species being a multiple of 3.
(Please pardon my poor use of English)
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wowbagger
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Re: Chameleon island
« Reply #4 on: Mar 31st, 2003, 5:44am » |
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More mathematically speaking, the three differences di between the numbers of chameleons of different colours aren't altered by the colour-changing when taken modulo 3.
In the beginning, all di = 1 (mod 3). (Or 2, depending on which you subtract. The important thing is that di != 0 (mod 3).)
If there's only one colour left, the difference between the other two is dj = 0. However, this value cannot be attained by the process.
quod erat demonstrandum.
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| « Last Edit: Mar 31st, 2003, 5:50am by wowbagger » |
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