# Alice and Bob Marble Fight - Part 3

Probability Level 2

Alice and Bob are at either end of a (really long) track, whose width is the diameter of a marble. 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 on the track, 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

• All marbles move at the same speed.
• All the marbles are of the same mass,
• All the collisions are perfectly elastic, meaning that they will bounce back at the same speed.
• There isn't space for the marbles to "pass over" each other. They will collide on the track.
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