# 203 geometry/topology/fixed.point.p

## Description

This article is from the Puzzles FAQ, by Chris Cole chris@questrel.questrel.com and Matthew Daly mwdaly@pobox.com with numerous contributions by others.

# 203 geometry/topology/fixed.point.p

A man hikes up a mountain, and starts hiking at 2:00 in the afternoon
on a Friday. He does not hike at the same speed (a constant rate), and
stops every once in a while to look at the view. He reaches the top in
4 hours. After spending the night at the top, he leaves the next day
on the same trail at 2:00 in the afternoon. Coming down, he doesn't
hike at a constant rate, and stops every once in a while to look at the
view. It takes him 3 hours to get down the mountain.

Q: What is the probability that there exists a point along the trail
that the hiker was at on the same time Friday as Saturday?

You can assume that the hiker never backtracked.

geometry/topology/fixed.point.s

100%. Superimpose the days: Friday starts walking up at 2:00,
Saturday starts walking down at 2:00. Since they are on the same
path, they must meet.

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