Eight persons P to Wsit around a rectangular table in such a way that ...
Seating Arrangement Analysis
To solve the seating arrangement of persons P to W at the rectangular table, we can follow these steps:
1. Table Configuration
- The table has 8 seats: 3 on each longer side and 1 on each shorter side.
- Longer sides: A, B, C (left to right)
- Shorter sides: D (top) and E (bottom)
2. Placement of Q and S
- Since neither Q nor S sits along the longer sides, they must occupy the shorter sides.
- Possible configuration: Q at D and S at E (or vice versa).
3. Positioning of P and V
- P is seated third to the left of V. Since P cannot be adjacent to Q or S, the only possible configuration is:
- V (long side) - P (long side, third left)
4. Determine W and U's Positions
- W sits opposite U and is not adjacent to P.
- Given P's position on the long side, U must also be on the opposite side of the table (long side), while W sits directly opposite U.
5. Placing T
- T is adjacent to neither V nor S, limiting T's options on the long side not occupied by P or V.
- T will occupy the remaining spot on the long side.
6. Final Arrangement
- The finalized seating arrangement from one perspective:
- Longer Side A: P, (empty), (empty)
- Longer Side B: V, T, (empty)
- Short Side D: Q
- Short Side E: S
- Longer Side C: W, U, (empty)
This arrangement satisfies all conditions provided in the question.
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