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Chameleon Island (Posted on 2009-09-25) Difficulty: 3 of 5
On Chameleon Island exists a peculiar sort of chameleon. At any given time any given chameleon is either red, blue or green. When two chameleons of unlike color meet, both immediately change to the remaining possible color.

I scientist has collected 36 of these animals, 12 of each color, and kept them in 36 separate containers to prevent color change, but he wants to keep them in two terraria.

When kept together in small numbers, there's a danger that all the lizards will ultimately go to one color, as exemplified by the following scenario starting out with 1 red, 4 blue and 13 green chameleons. The two letters at the left of each line specify the meeting that changed the count to the one on the given line:


      r  b  g
      1  4 13
rg    0  6 12
bg    2  5 11
rg    1  7 10
rg    0  9  9
bg    2  8  8
bg    4  7  7
bg    6  6  6
bg    8  5  5
bg   10  4  4
bg   12  3  3
bg   14  2  2
bg   16  1  1
bg   18  0  0

From then on, this scenario has all 18 of its chameleons red.

How can the scientist divide his 36 chameleons between the two terraria without posing the possibility of all becoming one color in either terrarium? Assume that no births or deaths occur. There's more than one way.

See The Solution Submitted by Charlie    
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Comments: ( You must be logged in to post comments.)
  Subject Author Date
Mind your Mods; Pare your Parityed bottemiller2009-09-25 17:56:59
SolutionThe key to solutionJer2009-09-25 15:27:02
Hints/TipsVery interesting (hints / thoughts)Steve Herman2009-09-25 14:03:26
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