The monk problem

The monk problem (Duncker, 1945)

One morning a Buddhist monk sets out at 5am on a Monday to climb a path up the mountain to reach the temple at the summit. He arrives at the temple at 2pm. Exactly 3 days later, he leaves the temple at 5am to descend the mountain, traveling somewhat faster since it is downhill. Show that there is a spot along the path that the monk will occupy at precisely the same time of day on both trips.

In attempting to solve this problem, try to separate the signal from the noise: The signal is the meaningful information that you’re actually trying to detect. The noise is the random, unwanted variation or fluctuation that interferes with the signal.