Students and Subjects
Source: Junior Olympiad of Malaysia Shortlist 2015 C6
July 17, 2015
combinatorics
Problem Statement
In a massive school which has students, and each student took at least one subject. Let be an odd prime. Given that:(i) each student took at most subjects. \\
(ii) each subject is taken by at most students. \\
(iii) any pair of students has at least subject in common. \\Find the maximum possible value of .