On a particularly strange railway line, there is just one infinitely long track, so overtaking is...

On a particularly strange railway line, there is just one infinitely long track, so overtaking
is impossible. Any time a train catches up to the one in front of it, they link up to form a
single train moving at the speed of the slower train. At first, there are three equally spaced
trains, each moving at a different speed. After all the linking that will happen has happened,
how many trains are there? What would have happened if the three equally spaced trains
had started in a different order, but each train kept its same starting speed? On average
(where we are averaging over all possible orderings of the three trains), how many trains will there be after a long time has elapsed? What if at the start there are 4 trains (all moving
at different speeds)? Or 5? Or n? (Assume the Earth is flat and extends infinitely far in all
directions.)

Expert Solution

Colby Messinger answered 6 months ago

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