On an island, there are 2020 chameleons. Among them, there used to be 800 blue chameleons, 1000 white chameleons, and 1220 red chameleons. Then, when two chameleons of different colors meet, they both change color and take on the third color. One day, Felix the pirate arrived on the island and discovered that all the chameleons were the same color. What was this color?
Let's find an invariant of the dynamical system presented here. If we denote $a, b$, and $c$ as the number of blue, white, and red chameleons on the island, then each color change will vary $a, b$, and $c$ by -1 or +2: since distinguishing these two cases would be cumbersome, let's content ourselves for now with noting that the values of these three integers vary by $+1(\bmod 3)$. Thus, if there have been $k$ color changes in total, we actually count $k+2$ $(\bmod 3)$ blue chameleons, $k+1(\bmod 3)$ white chameleons, and $k+2(\bmod 3)$ red chameleons. In particular, when Félix arrives, it is impossible to have 2020 blue chameleons and no red chameleons, or vice versa. Therefore, there must have been 2020 white chameleons.