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.
Frequently asked questions
Does his walking speed matter?
No. As long as both journeys are continuous from 6am to 6pm, a crossing point is guaranteed regardless of pace or pauses.