Eight friends A, B, C, D, E, F, G and H are sitting in a circle facing the…
2024
Eight friends A, B, C, D, E, F, G and H are sitting in a circle facing the centre. B is sitting between G and D. H is third to the left of B and second to the right of A. C is sitting between A and G. B and E are not sitting opposite each other. Who is third to the left of D?
- A.
F
- B.
E
- C.
A
- D.
None of these
Show answer & explanation
Correct answer: A
Concept: In a circular seating puzzle, number the seats 1 to 8 clockwise. Since everyone faces the centre, moving to a person's left means moving to the next seat in the clockwise direction, and moving to their right means moving to the next seat in the counter-clockwise direction; "X sits between Y and Z" means X's two neighbours are exactly Y and Z. Fix one person as an anchor, derive the rest from the directional clues in sequence, then use any elimination clue to remove the last ambiguity.
Applying it to this arrangement:
Fix B at seat 1 as the anchor.
H is third to the left of B (left = clockwise): seat of H = 1 + 3 = seat 4.
H is second to the right of A (right = counter-clockwise): seat of A = seat of H + 2 = 4 + 2 = seat 6.
B sits between G and D, so G and D occupy the two seats next to B, seats 8 and 2, in an order to be fixed later.
C sits between A and G: since C must be adjacent to A (seat 6), C can only be at seat 5 or seat 7. G is either seat 8 or seat 2 (from the previous step). If G were at seat 2, G's neighbours would be seats 1 and 3, which share no seat with C's candidate seats (5 or 7) — so this case is impossible. G must instead be at seat 8, whose neighbours are seats 7 and 1; seat 7 matches one of C's candidate seats, so C is at seat 7, and D — the other neighbour of B — takes the remaining seat, seat 2.
Seats 3 and 5 remain for E and F. B and E are not sitting opposite each other; the seat opposite B (seat 1) is seat 5, so E cannot take seat 5 — E is at seat 3 and F is at seat 5.
This gives the complete arrangement:
Seat | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
Person | B | D | E | H | F | A | C | G |
Cross-check against every clue:
B (seat 1) sits between G (seat 8) and D (seat 2) — holds.
H (seat 4) is third to the left of B (1 + 3 = 4) — holds.
H (seat 4) is second to the right of A (4 + 2 = 6, so A = 6) — holds.
C (seat 7) sits between A (seat 6) and G (seat 8) — holds.
B (seat 1) and E (seat 3) are not opposite each other, since the seat opposite B is seat 5 — holds.
D is at seat 2. Third to the left of D = seat 2 + 3 = seat 5, which is F.