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Changing Chameleons (Posted on 2002-04-19) Difficulty: 4 of 5
At one point, a remote island's population of chameleons was divided as follows:
  • 13 Red chameleons
  • 15 Green chameleons
  • 17 Blue chameleons
Each time two different colored chameleons would meet, they would change their color to the third one. (I.E. If Green meets Red, they both change their color to Blue.)

Is it ever possible for all chameleons to become the same color? (Why or why not?)

  Submitted by levik    
Rating: 4.1250 (16 votes)
Solution: (Hide)
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.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Unlimited optionsDrew2003-10-09 00:22:03
easyrichie2003-01-25 18:02:35
Incredibly SimpleMike2002-05-10 15:07:50
Spoilers.Paul Brinkley2002-04-22 07:56:33
I know the answer...levik2002-04-20 15:53:00
i think its not possiblesariz2002-04-20 14:32:52
Oops!!Sharky2002-04-20 13:27:39
I think Im right..Sharky2002-04-20 13:24:48
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