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This was never actually answered.
Can it be, as worded? I don't think so, since velocity isn't
necessarily a constant for the 2 trips. Average velocity is
the same, of course, since it took the same amount of time to
go up as it did to go down.
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| This was answered by Eric. It's got nothing to do with velocity. It's
just an application of the Intermediate Value Theorem. Now it actually
takes a lot of mathematics to *prove* that theorem, but the result is
intuitively obvious, and I think the idea of this puzzle is just to get
to a point where you can see why the result is obvious.
Our traveller is going up the hill, starting at 8am from the bottom.
Imagine that there is another traveller who starts from the top of the
hill going down at the same time, 8am. Then however they vary their
speed, and backtrack, and delay, we do know that by 8pm, each has
reached his destination. It is "obvious" that at some point they must
have passed, and at that point they were both at the same place on the
mountain at the same time.
The rest of the puzzle is just a complication that the "another
traveller" is actually a "phantom" appearing 24 hours before he
actually walks down the mountain. In the era of "X-Files" we should
have no difficulty dealing with this complication, which does not
affect the answer.
Cheers,
Andrew.
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