Creativity Studies

text and animation from Nyiri: The Picture Theory of Reason

[Here is] a puzzle readers of Arthur Koestler will be familiar with.
(Koestler, The Act of Creation, London: Hutchinson, 1964, pp.183f. Koestler refers to the June 1961 issue of Scientific American as his source, but remarks that the problem originates with the psychologist Carl Duncker)

One morning, exactly at sunrise, a Buddhist monk began to climb a tall mountain. The narrow path, no more than a foot or two wide, spiralled around the mountain to a glittering temple at the summit. - The monk ascended the path at varying rates of speed, stopping many times along the way to rest and to eat the dried fruit he carried with him. He reached the temple shortly before sunset. After several days of fasting and meditation, he began his journey back along the same path, starting at sunrise and again walking at variable speeds with many pauses along the way. His average speed descending was, of course, greater than his average climbing speed. - Prove that there is a single spot along the path the monk will occupy on both trips at precisely the same time of day.

Koestler liked to put this problem to his friends. The conclusion the mathematically minded among them tended to come to was that it would be an unlikely coincidence if the monk happened to be at the same spot at the same time of the day in the course of such two different journeys. Others however saw the solution. These are the words of "a young woman without any scientific training":

I tried this and that, until I got fed up with the whole thing, but the image of the monk in his saffron robe walking up the hill kept persisting in my mind. Then a moment came when, superimposed on this image, I saw another, more transparent one, of the monk walking down the hill and I realized in a flash that the two figures must meet at some point some time - regardless at what speed they walk and how often each of them stops. Then I reasoned out what I already knew: whether the monk descends two or three days later comes to the same; so I was quite justified in letting him descend on the same day, in duplicate so to speak.