Chameleons of three colorsDiscrete Mathematics Level 2
On the island of Camelot live 13 gray, 15 brown and 17 crimson chameleons. If two chameleons of different colors meet they both simultaneously change color to the third color (e.g. if a gray and a brown chameleon meet each other they both change to crimson).
(a) Is it possible that they will eventually all be the same color?
(b) Is it possible that there will eventually be the same numbers of gray, brown, and crimson chameleons?
(1984 Tournament of Towns, Problem 1)