You hike up a mountain trail, starting from the bottom at 9:00 AM and reaching the top at 5:00 PM. As you hike up the trail, you vary your pace, stop to rest on several occasions, and take a break for lunch. But you always stay on the trail.
After spending the night at the top of the mountain, you hike down the same trail the next day. You begin your descent at 9:00 AM and reach the bottom at 5:00 PM. Again, you vary your pace, stop to rest, and take a break for lunch, but you always remain on the trail.
The problem is the following. Were you ever at the same place on the trail at exactly the same time on each of the two days? Could you have walked down the trail on the second day so that you were never at the same spot at the same time of day? Or must you have been at the same spot at the same time of day no matter how you walked down the trail?
