I've found this problem in a math contest. Apparently it's solved by group theory but I have no idea how.
We're playing a game with a set of red and blue marbles arranged in a line.
Here are the rules of the game:
A blue marble can jump over two red marbles and kills one of the two.
A marble (blue or red) can jump over three adjacent red marbles and kills the three.
A marble (blue or red) can jump over two adjacent blue marbles and kills both.
Suppose that at the initial state we have $2007$ blue marbles, $2008$ red marbles and again $2007$ blue marbles arranged in a line.
Is it possible to reach a state when only blue marbles are left?