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Students and Subjects

Source: Junior Olympiad of Malaysia Shortlist 2015 C6

July 17, 2015
combinatorics

Problem Statement

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.