Question

On a 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. You watch, and eventually (after all
the linking that will happen has happened), you count the trains. You wonder what
would have happened if the trains had started in a different order (but each of the
original three trains had kept its same starting speed). On average (averaging over all
possible orderings), 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?


Specifically, what is the answer for n? I have the rest.

Thank you so much in advance!

Answer 1

Answer:

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