Section Capacity Analysis

The problem requires finding a section where students can be seated in three rows with an alternating boy-girl pattern, ensuring the first and last seats in each row are occupied by boys.

• Let $N$ be the total number of students in a section.
• There are 3 rows ($R=3$).
• Let $n$ be the number of students per row. Total students $N = R \times n = 3n$.
• The seating arrangement is alternating (B G B G...).
• Crucially, the first and last positions in each row must be occupied by boys (B).

Row Pattern Logic

• For the first and last seats to be boys in an alternating pattern, the total number of seats in each row ($n$) must be odd.
• Example: If $n=5$, the pattern is B G B G B. Boys occupy seats 1, 3, 5. Girls occupy seats 2, 4. This fits the condition.
• If $n$ were even, say $n=4$, the pattern would be B G B G. The last seat is occupied by a girl, contradicting the condition.
• Therefore, $n$ must be an odd number.

Total Students Calculation

• Since $N = 3n$ and $n$ must be odd, the total number of students ($N$) must be a multiple of 3, and when divided by 3, the result ($n = N/3$) must be odd.

Evaluating Section Sizes

We check each section's total number of students ($N$) to see if $N/3$ is an odd number:

• Section A: $N=24$. $N/3 = 24/3 = 8$. 8 is even.
• Section B: $N=27$. $N/3 = 27/3 = 9$. 9 is odd. This section could meet the criteria.
• Section C: $N=30$. $N/3 = 30/3 = 10$. 10 is even.
• Section D: $N=36$. $N/3 = 36/3 = 12$. 12 is even.

Conclusion

Only Section B, with 27 students, results in an odd number of students (9) per row when divided equally among the 3 rows. This allows for the specified alternating seating arrangement where boys occupy the first and last positions in each row.