Let T be the operation "touch"; RC : {red chameleons}, and T(GC, YC) ->
{GC -1}, {YC -1}, {RC + 2}. You need to demonstrate the friendliness of the lizards: if they don't touch, they won't change color, and your scientist will be frustrated.
>
> John (gnujohn)
Lets assume that a green chameleon touches a yellow chameleon, then according to the scientist’s discovery, both chameleons will turn red. Thus, the number of green chameleons is reduced by 1, the number of yellow chameleons is reduced by 1 and the number of red chameleons is raised by 2; [ 1 (green) + 1 (yellow) = 2 (red) ]. The difference between the green and yellow chameleon would remain constant; [ {green, yellow, red} => {10, 14, 15} => {9, 13, 17} => {8, 12, 19}, hence, 10 - 9 = 1 & 9 - 8 = 1, therefore the differences remains constant ], and the difference between the green and red, yellow and red chameleon will increase by 3; [ e.g 15 - 10 = 5, 17 - 9 = 8, 8 - 5 = 3 ], if all of the green and red chameleons were to meet and change. When these differences are divided by 3, there will always be a remainder; [ differences % 3 != 0 ], hence this implies that it is impossible for all of the chameleons to be of the same colour, as there will always be a remaining chameleon of an outstanding colour.
