Here’s a quick puzzle that I don’t think has appeared here previously.
A man leaves at exactly 6:00 AM to climb a mountain. He may not climb at a constant rate. In fact, he may stop to rest, or even backtrack a bit to see something interesting. He arrives at the summit at exactly 6:00 PM and camps for the night.
The next day, he starts down at exactly 6:00 AM, again meandering unevenly, but following exactly the same path and reaching the bottom at exactly 6:00 PM.
The question is, was there some point on the path he was sure to have visited at exactly the same time on the two trips?