let the blue and green chameleon meet first. Result : 14 - red 14 - green 16 - blue now 14 times pair of red and green meet to make it all 44 blue
On Sep 5, 11:44 pm, Don <dondod...@gmail.com> wrote: > Yes, you are right, it is 4 in that case. It seems that f is always > even. It is possible for 44 chameleons to be one color, but then there > is only one left and it cannot change to that color. Any time there > are 43 chameleons of one color, the other two are the same color. > It is true that all the chameleons can never be the same color, but I > agree that his "proof" is not valid. > Don > > On Sep 5, 9:08 pm, wujin chen <wujinchen...@gmail.com> wrote: > > > > > hi Don, i think f(15,14,16) =|15-14|+|14-16|+|16-15| = 1+2+1=4, hou do you > > get f(15,14,16) = 5? > > > 2011/9/6 Don <dondod...@gmail.com> > > > > No, f(15,14,16) = 5. > > > Don > > > > On Sep 5, 8:33 pm, wujin chen <wujinchen...@gmail.com> 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~！ > > > > -- > > > You received this message because you are subscribed to the Google Groups > > > "Algorithm Geeks" group. > > > To post to this group, send email to algogeeks@googlegroups.com. > > > To unsubscribe from this group, send email to > > > algogeeks+unsubscr...@googlegroups.com. > > > For more options, visit this group at > > >http://groups.google.com/group/algogeeks?hl=en.- Hide quoted text - > > - Show quoted text - -- You received this message because you are subscribed to the Google Groups "Algorithm Geeks" group. To post to this group, send email to algogeeks@googlegroups.com. To unsubscribe from this group, send email to algogeeks+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/algogeeks?hl=en.
