The following is an unexpected riddle that originated from the fact that my Calculus teacher enjoys being mean with us, the students:
The fact that not all students in a class can be above the average grade is proof that, by the same criteria, not all can be below the average grade aswell; so, in a class with $n$ students that can obtain a grade from $0$ to $k$, $k \geqslant 0$, what is the maximum amount of students that can be above/below average?
n-1. Say n students get k, one poor unfortunate soul gets 0. The average, which I don't really even need to evaluate, is something between 0 and k. Hence, one below average, everyone else above. Similarly, we can consider the case with n-1 scoring 0, and one over achiever scoring k. By the given statement, we know that it can be no more than n-1, so it is the maximum.