Eight friends A, B, C, D, E, F, G and H are sitting around a circular table, all facing towards the center. Only B is between H and D. Only C is between H and E. E is fourth to the right of D. B is third to the right of E. Only F is between G and A. G is not adjacent to D. Who is sitting second to right of B?
A
Understanding Circular Seating Arrangements
This problem involves arranging eight friends around a circular table based on several clues. Everyone is facing the center of the table. Circular arrangement problems require careful step-by-step deduction to correctly place individuals relative to each other.
Breaking Down the Seating Clues
Let's analyze each statement to build the seating arrangement:
- "Eight friends A, B, C, D, E, F, G and H are sitting around a circular table, all facing towards the center." - This sets up the basic structure. There are 8 positions around the circle.
- "Only B is between H and D." - This means H and D are the immediate neighbors of B, one on each side. The sequence is either H-B-D or D-B-H.
- "Only C is between H and E." - Similarly, H and E are the immediate neighbors of C. The sequence is either H-C-E or E-C-H.
- "E is fourth to the right of D." - In a circle of 8, being fourth to the right means they are directly opposite each other. If we fix D's position, E is 4 steps clockwise from D.
- "B is third to the right of E." - This places B relative to E. Starting from E, move 3 steps clockwise to find B.
- "Only F is between G and A." - G and A are the immediate neighbors of F. The sequence is either G-F-A or A-F-G.
- "G is not adjacent to D." - G cannot be in the positions immediately next to D.
Step-by-Step Deduction of the Circular Arrangement
Let's use the strong positional clues first to build the structure:
- Place D and E: E is fourth to the right of D. Let's assume D is at position 1. Moving clockwise, E will be at position $1+4=5$. D and E are opposite.
- Place B: B is third to the right of E. E is at position 5. Moving clockwise from E: 1st right is 6, 2nd right is 7, 3rd right is 8. So, B is at position 8.
- Place H: Only B is between H and D. D is at position 1, B is at position 8. For B to be *between* H and D and be the *only* person, H must be adjacent to B on the other side of D. The positions adjacent to B (8) are 7 and 1 (D). Since D is already placed next to B, H must be at position 7. Let's check: Is B (8) between H (7) and D (1)? Yes, they are adjacent in the sequence ...H-B-D... (or D-B-H, depending on direction).
- Place C: Only C is between H and E. H is at position 7, E is at position 5. For C to be the *only* person between them, C must be adjacent to both H and E. The position between 7 and 5 (going clockwise from 7 to 5 is a long way; going counter-clockwise is shorter) is 6. So, C must be at position 6. Let's check: Is C (6) between H (7) and E (5)? Yes, H, C, and E are adjacent in sequence H-C-E.
- Determine Remaining Positions: So far, we have placed D(1), B(8), E(5), H(7), and C(6). The remaining positions are 2, 3, and 4. The remaining friends are A, F, and G.
- Place A, F, and G: Only F is between G and A. This means G, F, and A must occupy the remaining consecutive positions 2, 3, and 4 in the sequence G-F-A or A-F-G. So, either G=2, F=3, A=4 OR A=2, F=3, G=4.
- Apply the last constraint: G is not adjacent to D. D is at position 1. The positions adjacent to D are 2 and 8. G cannot be at position 2. From step 6, G must be at 2 or 4. Since G cannot be at 2, G must be at 4. If G is at 4, then F must be at 3 and A must be at 2 to maintain the A-F-G or G-F-A sequence in positions 2, 3, 4. The only sequence that fits is A at 2, F at 3, G at 4 (A-F-G).
- Final Arrangement: Let's list the friends in clockwise order starting from position 1:
Position 1: D
Position 2: A
Position 3: F
Position 4: G
Position 5: E
Position 6: C
Position 7: H
Position 8: B
The circular arrangement clockwise is D-A-F-G-E-C-H-B.
Visualizing the Final Seating Arrangement
| Position | Friend |
|---|---|
| 1 | D |
| 2 | A |
| 3 | F |
| 4 | G |
| 5 | E |
| 6 | C |
| 7 | H |
| 8 | B |
Answering the Question: Who is sitting second to right of B?
Now that we have the final arrangement, we can answer the question.
B is at Position 8.
- The person sitting first to the right (clockwise) of B (Position 8) is at Position 1, which is D.
- The person sitting second to the right (clockwise) of B (Position 8) is at Position 2, which is A.
Therefore, A is sitting second to the right of B.
| Steps Right of B | Position | Friend |
|---|---|---|
| 1st Right | 1 | D |
| 2nd Right | 2 | A |
Revision Table: Key Clues and Deductions
| Clue | Deduction |
|---|---|
| E is fourth to the right of D | D and E are opposite. If D is at 1, E is at 5. |
| B is third to the right of E | If E is at 5, B is at 8. |
| Only B is between H and D | Given D(1) and B(8), H must be adjacent to B and D. H is at 7. Sequence H-B-D. |
| Only C is between H and E | Given H(7) and E(5), C must be adjacent to H and E. C is at 6. Sequence H-C-E. |
| Only F is between G and A | A, F, G are consecutive in the remaining slots (2, 3, 4). Sequence A-F-G or G-F-A. |
| G is not adjacent to D | D is at 1, adjacent slots are 2 and 8. G cannot be at 2. |
| Combining A-F-G/G-F-A and G <not adjacent to D> | Sequence A-F-G fills slots 2, 3, 4. A at 2, F at 3, G at 4. This respects G not being at 2. |
| Final Arrangement | D(1), A(2), F(3), G(4), E(5), C(6), H(7), B(8) clockwise. |
Additional Information on Seating Arrangements
Seating arrangement puzzles are common in logical reasoning sections of competitive exams. Mastering these requires understanding directional relationships (left/right) in circular or linear setups and combining multiple constraints systematically.
- Circular vs. Linear: In linear arrangements, directions are absolute (left end, right end). In circular, directions are relative to the person's facing direction (usually center) or relative to another person.
- "Between": The phrase "X is between Y and Z" usually implies Y and Z are immediate neighbors of X. However, sometimes it can mean X is just somewhere along the path between Y and Z. The clue "ONLY X is between Y and Z" clarifies that Y and Z are X's immediate neighbors.
- Right/Left: When everyone faces the center of a circle, "right" means clockwise movement, and "left" means counter-clockwise movement.
- Opposite: In a circle with an even number of seats, 'Nth to the right' can mean opposite. For example, in an 8-person circle, 4th to the right is opposite. In a 6-person circle, 3rd to the right is opposite.
Practice with different numbers of people and varying constraints helps improve speed and accuracy in solving these logical reasoning problems.
Important Questions from Circular Arrangement
P, M, D, A, F, H, R and B are sitting around a circle facing at the centre. R is fourth to the right of A, who is third to the right of P. M is second to the left of H, who is second to the left of P. D is third to the right of B. Which of the following pairs are immediate neighbors of B?
Six people, K, L, M, N, O and P, are sitting on the ground in a hexagonal shape but not necessarily in the same order. K is not sitting next to L or M. N is not sitting next to M or O. L is the neighbour of M. P is in the middle of M and N. What is the correct order of seating positions of the people in clockwise direction?
Six friends, G, H I, J, K and L, are sitting around a circular table, facing towards the centre of the table. H is sitting third to the left of G. L and I are not neighbours of H. K is sitting to the immediate right of I. Who is sitting to the immediate left of L?
Eight friends A, B, C, D, E, F, G and are sitting around a circular table facing each other for a lunch. A is opposite F and third to the right of B. G is between F and D. H is to the left of D. E is between C and A. Who is sitting third to the right of A?
Six friends are sitting at equal distances from each other in a circle and facing the centre of the circle. Diraj is between Pramod and Parthiv. Priyanshu is between Mukund and Laya. Pramod and Mukund are opposite to each other. Laya is to the immediate left of Pramod. Who is sitting to the immediate left of Parthiv?
