OK, you're on an overnight mushroom-hunting trip which takes you up a mountain. You've heard that there is an enormous chaga mushroom at the top. You start up the mountain at 12 noon, and it takes you 4 hours to get to the top, which you therefore reach at 4 PM. It's getting dark, so you camp out overnight. You start going down the mountain the next day, beginning at the stroke of 12 noon once again. You take exactly the same route down, and it takes the same 4 hours. So it is again 4 PM when you are back where you started. Here's the question. Is there any moment when you pass exactly the same place at exactly the same time of day both going up and going down? Incidentally, you didn't find the chaga.