There was a young monk who sought spiritual clarification by climbing to the top of a steep mountain. She embarked at sunrise, following a winding path wide enough for only one person, stopping occasionally along the way to rest or eat. By sundown she reached the mountain-top. She meditated there that night, and the entire next day. The following morning, at sunrise, she began the journey down along the same narrow path she had used for her ascent, again stopping intermittently for food and rest.

Assuming that she left at precisely the same time on both treks and returned to the same spot, can you prove (or disprove) that there is some place along the path that she passed at exactly the same time of day on both journeys?