MathDB

There are

n^2

students in a class. Each week all the students participate in a table quiz. Their teacher arranges them into

n

teams of

n

players each. For as many weeks as possible, this arrangement is done in such a way that any pair of students who were members of the same team one week are not in the same team in subsequent weeks. Prove that after at most n\plus{}2 weeks, it is necessary for some pair of students to have been members of the same team in at least two different weeks.

Problem Statement