Solution Step 0/0
One morning a Buddhist monk sets out at sunrise to climb a path up the mountain to reach a glittering temple at the summit. The narrow path, no more than a foot or two wide, spirals around the mountain. The monk ascends the path at varying rates of speed, stopping many times along the way to rest and eat the dried fruit he carried with him. He arrives at the temple just before sunset.
After several days of fasting, he begins his journey back along the same path, starting at sunrise and again walking at variable speeds with many pauses along the way, traveling somewhat faster since it is downhill.
Is there a simple way to prove that there is a spot along the path that the monk will occupy on both trips at precisely the same time of day?
After several days of fasting, he begins his journey back along the same path, starting at sunrise and again walking at variable speeds with many pauses along the way, traveling somewhat faster since it is downhill.
Is there a simple way to prove that there is a spot along the path that the monk will occupy on both trips at precisely the same time of day?
Explanations
Yes, there is an elegant proof for this challenge, requiring just the inclusion of a 2nd monk. One monk departs at sunrise from the foothill walking up the path, while another departs at the same sunrise from the summit walking down. The two monks must meet somewhere on the trail, therefore occupying the same spot on the trail at the same time of day.[After Duncker, 1945]
Check Yes, with a watch
Check Yes, with a 2nd monk
Check Yes, with a compass
Check No, needs more data
