2・108 In a class of 30 students, each student has the same number of friends within the class. How many students at most can there be who are better than the majority of their friends in terms of academic performance (assuming that for any two students in the class, it can be determined who performs better)?
[Solution] Answer: 25 students.
In fact, students who perform better than the majority of their classmates are referred to as "good students." Let the class have $x$ "good students," and each student has $k$ friends in the class.

Obviously, the student with the best grades in the class is the better performer in $k$ "friend pairs"; and by the given condition, each of the other "good students" is the better performer in at least $\left[\frac{k}{2}\right]+1 \geqslant \frac{k+1}{2}$ "friend pairs." Therefore, the "good students" are the better performers in at least
$$k+(x-1) \cdot \frac{k+1}{2}$$

"friend pairs." However, the total number of "friend pairs" in the class is $\frac{30 k}{2}=15 k$, so
$$\begin{array}{l}
k+(x-1) \frac{k+1}{2} \leqslant 15 k, \\
x \leqslant 28 \cdot \frac{k}{k+1}+1 .
\end{array}$$

Noting that the number of students who perform worse than the worst "good student" is at most $30-x$, therefore
$$\begin{array}{l}
\frac{k+1}{2} \leqslant 30-x \\
k \leqslant 59-2 x
\end{array}$$

From (1) and (2), we get
$$x \leqslant 28 \cdot \frac{59-2 x}{60-2 x}+1$$

which simplifies to
$$x^{2}-59 x+856 \geqslant 0$$

Noting that $x \leqslant 30$, it follows that the largest integer $x$ satisfying (3) is $x=25$. That is, the total number of "good students" does not exceed 25.

On the other hand, if all students in the class are ranked from best to worst and numbered 1 to 30, and these numbers are arranged in a $6 \times 5$ table (as shown). If two students in the class are friends if and only if their numbers fall into one of the following three cases:
(1) They are in adjacent rows but different columns;
(2) They are in the same column, with one at the bottom of the column;
(3) They are in the top row.
In this case, each student has 9 friends. And each of the students numbered 1 to 25 performs better than 5 of their friends. At this time, the total number of "good students" is 25.

In summary, the maximum number of students who perform better than the majority of their friends is 25.
\begin{tabular}{|c|c|c|c|c|}
\hline 1 & 2 & 3 & 4 & 5 \\
\hline 6 & 7 & 8 & 9 & 10 \\
\hline 11 & 12 & 13 & 14 & 15 \\
\hline 16 & 17 & 18 & 19 & 20 \\
\hline 21 & 22 & 23 & 24 & 25 \\
\hline 26 & 27 & 28 & 29 & 30 \\
\hline
\end{tabular}