Here is a little puzzle to think about.
The monk Gaito lives at the bottom of a hill just outside the ancient town of Huroko. One day, the monk leaves his home at 6:00am and makes his way up the hill along the narrow path that winds its way to the peak. The monk walks all day, occasionally stopping to rest and meditate, sometimes even retracing his steps for short distances, and arrives at the peak at 10:00pm. After spending the night fasting at the top, the monk starts the return journey at 6:00am the next morning and goes down the same narrow winding path, once again stopping occasionally or retracing his steps at various points along the way for contemplation. The monk returns to his home at the base of the hill at 10:00pm.
When you consider the monk’s two journeys, is it guaranteed that there will be at least one point along the path where the monk will be located at the same time during the day for both trips?
You can put your solutions and reasons in the comments.