Originally Posted by TGS
A Buddhist monk begins walking up a mountain at dawn one day. He reaches the summit at sunset, meditates at the top for several days until one dawn when he begins to walk back to the foot of the mountain, which he reaches at sunset. Making no assumptions about his starting or stopping or about his pace during the trips, can you prove that there is a place on the path which he occupies at precisely the same time of day on the two separate journeys.
He is at the start of the path at sunrise each day. Also, he is at the end of the path at sunset each day.