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.

###### Image credit: Wikipedia Leonardo Poletto

How many times do the marbles collide?

Assume that the marbles are of the same mass, and that the collisions are perfectly elastic. All marbles move at the same speed.

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