The Buddhist Monk Problem

At sunrise one morning, a Buddhist monk began to climb a tall mountain. The path was narrow, and it wound around the mountain to a beautiful, gleeming temple at the very top of the mountain.

The monk sometimes climbed the path quickly, and he sometimes went more slowly. From time to time, he also stopped along the way to rest or to eat the fruit he had brought with him. Finally, he reached the temple, just a few minutes before sunset. At the temple, he meditated for several days. Then he began his descent back along the same path. He left the temple at sunrise. As before, he walked slowly at times, but more quickly when the pathway was smooth. Again, he made many stops along the way. Of course, he walked down the hill more quickly than when he was walking up the hill.

Demonstrate that there must be a spot along the path that the monk will pass on both trips at exactly the same time of day. (The answer is found in Figure 11.1.)