Question 2 Let $n$ be a positive integer. Find the minimum value of $q=f(n)$ for which the following conclusion always holds: If $q$ students all participate in three mock exams of a mathematics competition, and each person's score in each exam is an integer from 0 to $n$, then there must be two students $A$ and $B$, such that for each exam, $A$'s score is not less than $B$'s score.
The answer to question 2 is $\left[\frac{3(n+1)^{2}+1}{4}\right]+1$