Solving the Circle Seating Arrangement Puzzle
This problem involves arranging six people (A, B, C, D, E, F) in a circle, all facing the center. We need to determine their positions based on given clues and find out who is sitting opposite A.
Step-by-Step Solution
1. Visualize the Circle Setup
Imagine a circle with six spots. We can number these spots 1 to 6 clockwise. Since everyone is facing the center, their left is in the clockwise direction, and their right is in the counter-clockwise direction.
2. Apply "B is second to left of A"
Let's place person A at position 1.
The direction to A's left (facing center) is clockwise.
The first spot to A's left is position 2.
The second spot to A's left is position 3.
So, B is seated at position 3.
3. Apply "C is opposite B"
In a circle with 6 people, the person opposite is 3 seats away. Since B is at position 3, the opposite position is $3 + 3 = 6$.
Therefore, C is seated at position 6.
4. Apply "D is between C and E"
This implies that C, D, and E are sitting in adjacent seats in the order C-D-E or E-D-C.
We know C is at position 6. The seats next to C are position 5 (clockwise) and position 1 (counter-clockwise).
We already placed A at position 1.
So, D must be in the seat next to C that is available. This means D is seated at position 5.
Since D (at 5) is between C (at 6) and E, E must be in the seat adjacent to D, other than C. The seats adjacent to D (at 5) are 4 and 6. C is at 6, so E must be seated at position 4.
5. Place the Remaining Person, F
We have assigned positions to A (1), B (3), C (6), D (5), and E (4).
The only person left is F, and the only position left is 2.
So, F is seated at position 2.
6. Final Arrangement Check
Let's confirm the seating arrangement:
| Position | 1 | 2 | 3 | 4 | 5 | 6 |
| Person | A | F | B | E | D | C |
Let's verify all the clues:
- Six people A-F in a circle, facing center: Checked.
- B is second to left of A: A is at 1, B is at 3. Checked.
- C is opposite B: B is at 3, C is at 6. Checked.
- D is between C and E: C is at 6, D is at 5, E is at 4. Checked.
- F is not neighbour of A: A is at 1, neighbours are 2 and 6. F is at 2. This condition appears to be contradicted by the positions derived from the other clues. However, the positions derived satisfy all other conditions.
7. Identify Who is Opposite A
In the arrangement determined:
- A is at position 1.
- The position opposite position 1 is position 4.
- E is seated at position 4.
Therefore, E is opposite A.
Important Questions from Seating Arrangement (Notes)
- Five friends are sitting on a bench in the following order :
(i) P is sitting next to Q and R is next to S.
(ii) S is not sitting with T; T is on the extreme left hand side of the bench and R is on second position from the right hand side.
(iii) P is on the right hand side of Q and to the right side of T. (iv) P and R sitting together
Who is sitting exactly in the middle ? Seven people, C, D, E, F, L, M and N, are sitting in a row, facing north.
Only two people sit to the right of C. Only two people sit between C and L. Only two people sit between E and N. N sits to the immediate left of C. M sits to the immediate right of F. Who sits at the third position from the left end of the row?- Seven people, A, B, C, D, E, F and G, are sitting in a row, facing north. Only three people sit between E and D. A sits to the immediate left of D. No one sits to the right of B. Only two people sit between B and A. G sits to the immediate right of F. How many people sit to the right of 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 A is kept above F. Only D is kept between F and C. Only E is kept below B. How many boxes are kept below C?
P, Q, R, S, T, U and V are sitting in a row, facing north. No one sits to the left of U. Only four people sit between U and R. Only three people sit to the right of V. P sits to the immediate left of S. Q is not an immediate neighbour of V. How many people sit between P and T?
