Ok, so we were a group of people and someone told a riddle that went something like this:
A man walks up a hill one day, following a trekking route. He begins at the foot of the hill at 7 am and reaches the top at 7 pm. The next day, he descends the hill, walking the exact same route, beginning at 7 am and finishing at 7 pm.
The route is naturally uneven, with steep, slow parts and more level, fast parts.
While descending the hill, will there be a point, anywhere, at any time, where he can say "Exactly at this time yesterday, I was here"?
In other words - is there sure to be a point that he reaches the same time both days?
I see myself as moderately intelligent - I did take some math courses in university, with probability and shit, but am far from a logical mastermind - but I had no problems whatsoever understanding this riddle, saying "yeah of course." However, almost nobody there, and almost nobody I've spoken about the riddle with, could see this solution.
Now, you guys are genuinely clever, so I'm turning to you. Is this riddle really that hard? Isn't the answer quite obvious - yes, there must exist such a point, regardless of his pace, and regardless of the terrain?