Chapter 2.C, Problem 15E

Alternative Thinking: The Monk and the Mountain. A monk set out from a monastery in the valley at dawn. He walked all day up a winding path, stopping for lunch and taking a nap along the way. At dusk he arrived at a temple on the mountaintop. The next day the monk made the return walk to the valley, leaving the temple at dawn, walking the same path for the entire day, and arriving at the monastery in the evening. Must there be at least one point along the path that the monk occupied at the same time of day on both the ascent and descent? (Source: The Act of Creation, Arthur Koestler)