The Grey Labyrinth is a collection of puzzles, riddles, mind games, paradoxes and other intellectually challenging diversions. Related topics: puzzle games, logic puzzles, lateral thinking puzzles, philosophy, mind benders, brain teasers, word problems, conundrums, 3d puzzles, spatial reasoning, intelligence tests, mathematical diversions, paradoxes, physics problems, reasoning, math, science.

Ghost Post · Icarian Member

sorry, if you guys have talked about this before, but i'm new to the GL so bare with me. In #4 of potpurri III, why is the answer yes? This assumes that the rate of descent is equal and constant to the rate of ascent. Can someone clear this up?

Quailman · His Postmajesty

The question: A climber leaves camp at midnight for the top of the mountain and arrives there at noon. He immediately turns around and climbs back down by the same route to arrive at camp at midnight, exactly 24 hours after he left it. Is it necessarily the case that at a point on the route his watch's hands were in the same position on the ascent as on the descent?

The Minotaur's answer: Yes, if you imagine two explorers on the same day, one starting at the summit, the other starting at base, they will pass each other at some point. At that point, their watches will read the same.

My reply: Your question about this problem seems to imply that the point at which this occurs is the halfway point. Where it occurs is not important. The fact is that somewhere along his route, the watch hands will be in the same position (as in the case of two climbers in opposite directions on the same day.