MathDB

C6

Part of JOM 2015 Shortlist

Problems(1)

Students and Subjects

Source: Junior Olympiad of Malaysia Shortlist 2015 C6

7/17/2015
In a massive school which has mm students, and each student took at least one subject. Let pp be an odd prime. Given that:
(i) each student took at most p+1p+1 subjects. \\ (ii) each subject is taken by at most pp students. \\ (iii) any pair of students has at least 11 subject in common. \\
Find the maximum possible value of mm.
combinatorics