Question 91
Let $n$ and $k$ be integers with $n\geqslant3$. Théo organizes the election of class representatives for his class of $n$ students. Each student must vote for one of their classmates (everyone is a candidate), and nobody votes for themselves. Théo then divides the students into groups so that no student is in the same group as the student they voted for.
For which values of $k$ is Théo certain to be able to divide the students into at most $k$ groups, regardless of how they vote?
For which values of $k$ is Théo certain to be able to divide the students into at most $k$ groups, regardless of how they vote?