Optimise The Students

Probability Level 5

A literature examination has n 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 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 n .

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