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
Seven friends, Subhi, Prince, Ketan, Vishal, Mahima, Krish and Naitik, are sitting around a circular table with their backs towards the centre. Subhi is sitting to the immediate right of Prince. Naitik and Krish are not sitting to the immediate left or right of Vishal. Vishal is sitting third to the left of Prince. Mahima is sitting to the immediate right of Vishal. Who is sitting third to the right of Prince?
Raghav, Manpreet, Sunaina, Prakrit, Vedika and Arwa are sitting around a circular table facing the centre. Raghav is second to the left of Prakrit. Manpreet is to the immediate left of Sunaina. Arwa is second to the right of Vedika. There are an equal number of persons between Raghav and Manpreet from both the ends. Who is sitting third to the left of Sunanina?
Five friends, Vishnu, Chirag, Raina, Kavya and Surbhi, are sitting around a circular table, facing the center. Vishnu is to the immediate right of Kavya. Chirag is third to the left of Kavya. Surbhi is not adjacent to Chirag. Who is second to the left of Kavya?
Six friends, David, Bhanu, Minto, Krita, John and Nisan, are sitting in a circle with their backs towards the centre. David and Minto are sitting to the immediate left and right of Bhanu, respectively. John is not sitting to the immediate left of David. Nisan is sitting third to the right of Bhanu. Who is sitting second to the left of Bhanu?
Eight friends, P, Q, R, S, T, U, V and W, are sitting in the same order anticlockwise around a circular table at equal distance between them, with all centre of the table. If Q is sitting in the south-east, then in which direction is W sitting?
