Alice and Bob are at either end of a (really long) track. Alice has 30 marbles and Bob has 20 marbles. They send all of their marbles towards each other in quick succession. Whenever 2 marbles collide they will just bounce back and start traveling in the opposite direction.

How many marbles does Alice end up with?

Assume that the marbles are of the same mass, and that the collisions are perfectly elastic.

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