# Optimise The Students

**Discrete Mathematics**Level 5

A literature examination has \( n \) candidates and 5 passage-based questions. For each question, each candidate is given a positive integer score which is at most 7. (They are copying the IMO. However, note here that the graders are nice. They refuse to give \( 0 \) marks.) It turns out that none of them were ideal literature students, since no pair of candidates had the same score on 2 different questions. Find the largest possible value of \( n \).