The Interesting Test - Answer 3

A man starts walking up a narrow mountain path at 6:00 a.m. He walks at different speeds, stopping to eat, sometimes going back a few steps to look at a flower, but never leaving the path. He eventually arrives at the top at 10:00 p.m. the same day. He camps out over night and starts down the same path at 6:00 a.m. the next day. After stopping to eat and so forth he arrives at the bottom at 10:00 p.m.

True or False: There is some point on the path that the man occupied at exactly the same time on the two different days. Explain your answer.


True
Imagine that on the first day a clone of the man starts down the mountain at 6:00 a.m. and arrives at the bottom by 10:00 p.m. The man and the clone have to pass each other at some point.


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