8. Let $n$ students be such that among any 3 of them, 2 know each other, and among any 4 of them, 2 do not know each other. Find the maximum value of $n$.
(Tang Lihua
8. The maximum value of $n$ is 8.

When $n=8$, the example shown in Figure 7 satisfies the requirements, where $A_{1}, A_{2}, \cdots, A_{8}$ represent 8 students, and the line between $A_{i}$ and $A_{j}$ indicates that $A_{i}$ and $A_{j}$ know each other.

Suppose $n$ students meet the requirements of the problem, we will prove that $n \leqslant 8$. For this, we first prove that the following two cases are impossible.
(1) If a person $A$ knows at least 6 people, denoted as $B_{1}, B_{2}, \cdots, B_{6}$, by Ramsey's theorem, among these 6 people, either there exist 3 people who do not know each other, which contradicts the given condition that any 3 people have 2 who know each other; or there exist 3 people who all know each other, in which case, $A$ and these 3 people form a group of 4 people who all know each other, which also contradicts the given condition.
(2) If a person $A$ knows at most $n-5$ people, then there are at least 4 people who do not know $A$, thus, these 4 people must all know each other, which is a contradiction.

Secondly, when $n \geqslant 10$, either (1) or (2) must occur, so $n$ does not meet the requirements at this time.

When $n=9$, to make (1) and (2) not occur, each person must know exactly 5 other people. Thus, the number of friend pairs (pairs of people who know each other) generated by these 9 people is $\frac{9 \times 5}{2} \notin \mathbf{N}_{+}$, which is a contradiction.
From the above, we know that the $n$ that meets the requirements is $\leqslant 8$.
In summary, the maximum value of $n$ is 8.