Finding invariants

Question

If in a given ecosystem there are 30 chameleons living on an island: 15 red, 7 blue, 8 green. When two of a different color meet, they both change into a third color (ie. if a red and blue meet, they both change into green chameleons). When two of the same color meet, they change into both of the other colors (ie. if two greens meet, one become red and the other becomes blue). Is there a state such that all of the chameleons will be red? Not sure how to figure out what invariant there is in common in all the states! I'm told to consider the remainders of the totals of each color when you divide by 3

Answer 1

Is there any way to ever get the number of Blue and Green the same? Here are the only possible events

$$\begin{array}{|c|c|c|c|} \hline \text{EVENT}& \text{RED}& \text{BLUE}& \text{GREEN} \\ \hline \text{Red meets Red}& \text{-2}& \text{+1}& \text{+1} \\ \hline \text{Blue meets Blue}& \text{+1}& \text{-2}& \text{+1} \\ \hline \text{Green meets Green}& \text{+1}& \text{+1}& \text{-2} \\ \hline \text{Blue meets Green}& \text{+2}& \text{-1}& \text{-1} \\ \hline \text{Red meets Green}& \text{-1}& \text{+2}& \text{-1} \\ \hline \text{Red meets Blue}& \text{-1}& \text{-1}& \text{+2} \\ \hline \end{array}$$