Overview
The monk puzzle sounds like it needs the monk's exact schedule, but the answer needs none of it — just the fact that two continuous journeys must cross.
How to solve The Monk on the Mountain
- Imagine both trips — the ascent and the descent — happening on the same day.
- One traveller starts at the base, the other at the summit, walking toward each other on one trail.
- Two people moving along the same path in opposite directions must meet — and the meeting is the shared time-and-place.
The key insight
Superimpose the two days. The gap 'ascent position minus descent position' starts negative and ends positive, so by the intermediate value theorem it is zero somewhere — a guaranteed crossing.
Variations & echoes
- It's a beloved intuitive illustration of the intermediate value theorem.
- The same argument proves antipodal points with equal temperature exist on Earth.