MathDB

Let natural

n \ge 2

be given. Let Laura be a student in a class of more than

n+2

students, all of which participated in an olympiad and solved some problems. Additionally, it is known that:
[*] for every pair of students there is exactly one problem that was solved by both students; [*] for every pair of problems there is exactly one student who solved both of them; [*] one specific problem was solved by Laura and exactly

n

other students.
Determine the number of students in Laura's class.

Problem Statement