Colour Changing

An island is inhabited by 45 chameleons of 3 varieties: 13 are blue, 15 green, and 17 purple. Two chameleons of different colors (blue and green, say) change to the third color (purple) if they meet. Can they all end up of the same color?

Answer:

No... Here's why:
In any encounter, the difference between two given varieties will stay the same, or be either increased or decreased by 3. Thus, two colors could be eradicated only if their initial difference was a multiple of 3...