Here's the puzzle of the month for November 2015:
A hiker starts at the base of a mountatin at 8 am and walks up the only path to the top, arriving at 6 pm. She takes rest stops on the path from time to time, and varies her speed based on the steepness of the terrain and other factors, but does not stray from the path. She spends the night at the top. On the next day, she walks down the same path, again starting at 8 am and arriving at 6 pm. Again, she varies her speed and takes rests as needed, not necessarily at the same places or for the same lengths of time as on the way up.
Find a simple explanation for the fact that it is absolutely certain that there is some point along the path that the hiker passed at exactly the same time of day on the way up as on the way down.
For a hint, go to the page Monthly Brainteaser Hint.
For the solution, go to the page Monthly Solution.