No, f(15,14,16) = 5. Don On Sep 5, 8:33 pm, wujin chen <[email protected]> wrote: > hi all, i encountered this puzzle (http://www.crackpuzzles.com/?p=236): > > 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?" > > and the solution provided by auther is like this: > *Solution: * > Lets define a function f(red, blue, green) = |red - blue| + |blue - green| + > |green - red| > When two chameleons of different colours meet and convert to the third one, > the value of function f will always change by 0 or 3 or 6 (i.e. a multiple > of 3). In the initial situation f is 8. > If all of them get converted into a single colour then f would be 90 = > 2*(red+blue+green) > So we are basically looking for a solution to the equation: 8 + 3x = 90, > which has no integer solutions. Hence it is not possible. > > well, my problem is this: > > f(13,15,17)=8, > f(15,14,16)=2 > so , we can see that " the value of function f will always change by 0 or 3 > or 6″ is not true, i am wondering~！
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