A, B, C, D, E and F are sitting around a round table. A is between E and F. E…
2013
A, B, C, D, E and F are sitting around a round table. A is between E and F. E is opposite to D and C is not in either of the neighbouring seats of E. The person opposite to B is
Answer: D. F — ConceptIn circular-seating problems, rotation and reflection do not change who is adjacent to or opposite whom. Fix one person at a reference seat, place…
- A.
C
- B.
D
- C.
A
- D.
F
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Correct answer: D
Concept
In circular-seating problems, rotation and reflection do not change who is adjacent to or opposite whom.
Fix one person at a reference seat, place opposite pairs, and then use adjacency restrictions to fill the remaining seats.
Application
Apply the constraints in this order:
Fix E at a reference seat; D must occupy the seat opposite E.
A is between E and F. Therefore place A next to E and F on A's other side. The mirror layout gives the same relationships.
The two remaining consecutive seats belong to B and C. Since C cannot be adjacent to E, C takes the remaining non-neighbouring seat and B takes the other seat.
The completed circle has the opposite pairs E–D, A–C, and B–F.
Cross-check
The resulting opposite pairs are recorded in the table:
Person | Opposite person |
|---|---|
E | D |
A | C |
B | F |
Reflecting the arrangement reverses its clockwise order but preserves every opposite pair, so the person opposite B is F.