An interesting riddle

[Adron]

Yes there are. Define "same height" as "within a single quanta(?) of the same height" and then, since the movement is a continuous function multiplied by a quantizing constant (as I would like to believe), you get the result easily using calculus as described.

If not, you'd have to look at the time, stretching and compressing with the changes of the hiker's velocity. This gets annoyingly complicated, stick to Newton mechanics for this please.

Sticking to Newton mechanics is proably safer. I don't think you can make this assumption at all without them. It's not a continous function multiplied by a quantizing constant, so you won't be getting the same height. You can probably safely say that he's been within one metre off the height he was at the previous day at the same time though.

An example of movement being discontinous should be tunneling.