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In a school there are

n

classes and

k

student. We know that in this school every two students have attended exactly in one common class. Also due to smallness of school each class has less than

k

students. If

k-1

is not a perfect square, prove that there exist a student that has attended in at least

\sqrt k

classes.
Proposed by Mohammad Moshtaghi Far, Kian Shamsaie Rated 4

Problem Statement