Here’s one from the textbook I used for calculus;
A hiker takes his time walking slowly and making many stops along a trail from 7:00 A.M. to 7:00 P.M. where he rests for the night. The next morning at 7:00 A.M. he begins his leisurely walk back along the exact same route, again making many stops along the way (not necessarily in the same places), and finishing at 7:00 P.M.
Is there for certain a place along the route where he was in that exact spot the same time on both days? The question isn’t asking where the particular spot is, only if such a particular spot exists.
(Hint: The answer book wanted required a minimal knowledge of function graphing, however this can be answered with no math background.)