chameleons we can sort of reduce the island, as far as what were concerned in, to a state machine. the state is described by 3 numbers, which represent the difference in population between R G B chameleons. ie at the start RG = -2, GB = -2, RB = -4 any meeting of chameleons is a transition in our state machine. in terms of state, we can generalize a transition t to the following transformation t { Num A = Num A Num B = Num B - 3 Num C = Num C - 3 } where the mapping of NumX to RG GB RB is determined by who meets who (try it) whatever the transitions you choose, the effect will be that of adding a multiple of 3 to the three state variables. so after any number of meetings RG = -2 + 3x, GB = -2 + 3y RB = -4 +3z where x y z are determined by what meetings occur. the island can be populated entirely by one color when any of the three numbers is zero, since at that point the two colors involved can cancel each other out and yield only the third color. in the language of the state machine this occurs when RG = 0  or GB = 0 o or RB = 0 so in conclusion RG = 0 and RG = -2 + 3x    or BG = 0 and RG = -2 + 3y    or RB = 0 and RB = -4 + 3z    or all which are unsatisfiable, so the answer is no. the other conclusion is that it would be possible if any of the differences between populations was a multiple of 3. hmm now that i read it, it looks like utter bullshit! hahahahah Cheradenine Zakalwe Wednesday, June 5, 2002 You can get all one color. Here's an example: Start with {13, 15, 17} A red meets a green, they both change to blue. Now we have {12, 14, 19} Same thing happens again and again . . . {11, 13, 21} {10, 12, 23} . . . . {0, 2, 43} Now, we have a blue meet a green, and get: {1, 1, 42} The red and green meet, and we're at: {0, 0, 44} So that's just proof by example.  Someone want to provide a more general proof? Andrew Hogue Tuesday, July 16, 2002 Where did you put the 45th lizard? Malachi Brown Friday, September 6, 2002   Fog Creek Home