13 green, 15 blue, and 17 red chameleons are on an island. Whenever two chameleons of different colors meet, they change to the third color. Is it possible for all of them to become the same color?
I said no. I took a look at all the chameleon numbers mod 3, and saw that they were 1 mod 3, 0 mod 3, and 2 mod 3. (I have some trouble explaining this part)->I did some color-changing on them, and saw that the chameleon numbers per color mod 3 stayed the same. The number of each color was either 0,1, or 2 mod 3. The number of chameleons of each color is either 0,1,2 mod 3, which doesn't change. so it is impossible to change everything to 0 mod 3. (all the colors have to have the same number in order to have everything become one color). I am not sure if I am going in the right direction or if this is the right proof.