Alice and Bob Marble Fight - Part 3

Discrete Mathematics Level 2

Alice and Bob are at either end of a (really long) track. Alice has 30 red marbles and Bob has 20 blue 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.

When all is said and done, how many red marbles does Bob end up with?

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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