At the OMM School every student goes to at least $k$ classes and two classes have at most $1$ student in common. Prove there is a set of $k$ classes where all of those classes have the same amount of students.
Thank you very much for reading. I have been having trouble finding ways to combine both of the requirements. I have tried looking at the students as sets of classes, classes as sets of students. I tried seeing it as several graphs to no avail. I also tried induction, but I think if it works we need a non-straightforward hypothesis.
Thank you very much in advance