The Way of the Monk - Solution

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Solution

Yes, there is such a spot (the exact spot depends on the details of how fast he goes).

Explanation

Imagine that there is a second monk as well. This second monk videotapes the exact steps that our first monk travels on the first day, and rushes down the mountain again during the night so that he is at the bottom of the trail on the morning of the second day.

Using the videotape and a portable video player, he then sets off at 06:00 on the second day and recreates the journey of the first monk exactly, except that it is 24 hours later.

Since, on the second day, the two monks leave at the same time and arrive at the same time, it's obvious that they must cross each other along the path at some spot. That spot is the spot when the first monk was at the same time on both days.

Note

For this explanation to be valid, I imagine that some deep property of the translatability of time must be true. This is beyond me.

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