A monk climbs a mountain in one day and descends the next, at varying speeds. Is there a point on the path he occupies at the exact same time on both days?

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A monk climbs a mountain trail on one day, starting at dawn and arriving at dusk, then descends the same trail the next day at a different pace, also from dawn to dusk. Is there a single point on the path he passes at exactly the same time of day during both trips?

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Answer

Yes — imagine both trips happening simultaneously on the same day; since one monk goes up and the other comes down on the same path, they must meet at some point, proving such a moment always exists.

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