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.
Important Questions from Puzzle (Notes)
- There are five men - A, B, C, D and E, six women P, Q, R, S, T and Z. A, B, and R are advocates. S, Q, P, D and C are doctors and the rest are teachers. A team has to be selected from these eleven persons subject to the following conditions:
(I) A, P and Z have to be together.
(II) B cannot go with D or R.
(III) E and Q have to be together.
(IV) C and T have to be together.
(V) D and P cannot go together.
(VI) C cannot go with Q.
If the team formed consists of two male advocates, two lady doctors and one teacher, the members of the team can be: - Seven boxes S, F, G, H, T and U are kept one over the other but not necessarily in the same order. Only two boxes are kept below S. Only one box is kept above U. Only one box is kept between U and B. G is kept immediately above F. T is kept at some place below H.
How many boxes are kept between H and G? - Seven boxes E, F, G, H, S, T and U are kept one over the other but not necessarily in themsame order. No box is kept above E. Only three boxes are kept between E and U. Only one box is kept between G and H. H is kept immediately above U. Only four boxes are kept between G and F. T is kept at some place above S. Which box is kept second below T?
- Seven boxes E, F, G, H, S, T and U are kept one over the other but not necessarily in the same order. H is kept immediately above E. T is kept immediately above U. Only F is kept above S. Only two boxes are kept above H. T is not kept at third position from the bottom.
How many boxes are kept between G and F? - Seven boxes A, B, C, D, E, F and G are kept one over the other but not necessarily in the same order.
Only two boxes are kept between D and E. Only F is kept above C. No box is kept below E. G is kept at some place below A but at some place above B.
How many boxes are kept below B?
