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Difficulty: HardSeating Arrangement

Eight colleagues—P, Q, R, S, T, U, V, and W—are seated around a circular table. Exactly four of them are facing the center, while the other four are facing outward (away from the center).

1. P sits third to the left of U, and both are facing the center.
2. T sits second to the left of P.
3. V and Q are immediate neighbors of each other, but neither is an immediate neighbor of P.
4. Q is not an immediate neighbor of U.
5. W sits second to the right of Q.
6. R sits second to the left of V.
7. The immediate neighbors of T face opposite directions (one faces the center, the other faces outward).

Based on the seating arrangement, which of the following statements is definitely TRUE?

  1. W sits to the immediate left of T, and both face outward.Answer
  2. B
    S sits second to the right of U, and they face opposite directions.
  3. C
    Q sits to the immediate left of V, and both face the center.
  4. D
    T sits to the immediate left of Q, and they face opposite directions.

Answer

The statement claiming that W sits to the immediate left of T, and both face outward, is definitely true.
Based on the completed arrangement, T is seated at position 6 and W is at position 5. Both face outward. For an outward-facing person, their left is in the counter-clockwise direction. Moving one position counter-clockwise from T (6) brings us to W (5). Therefore, W sits to the immediate left of T, and both face outward.

Step-by-Step Solution

1
Set up a circular layout with 8 numbered positions (1 to 8) moving clockwise.
Assume U is at position 1, facing the center.
Establishing a fixed anchor point simplifies relative positioning.
2
Place P and T using clues 1 and 2.
P is at position 4 (facing center) because left of U (center-facing) is clockwise. T is at position 6 because left of P (center-facing) is clockwise.
Direct directional application from the fixed anchor U.
3
Determine positions for V and Q using clues 3 and 4.
Neighbors of P (positions 3 and 5) cannot hold V and Q. The only adjacent open seats are 7 and 8. Since Q cannot be next to U (position 1), V must be at 8 and Q must be at 7.
Process of elimination based on adjacency constraints.
4
Determine W's position and Q's direction using clue 5.
W is 2nd to the right of Q(7). If Q faced outward, right would be clockwise (positions 8, 1), but U is at 1. Thus, Q faces the center, making right counter-clockwise (positions 6, 5). W is placed at position 5.
Deducing direction by testing which orientation allows a valid placement.
5
Determine R's position and V's direction using clue 6.
R is 2nd to the left of V(8). If V faced outward, left would be counter-clockwise (positions 7, 6), but T is at 6. Thus, V faces the center, making left clockwise (positions 1, 2). R is placed at position 2.
Similar to Step 4, V's direction is deduced by the availability of the target seat.
6
Place S and deduce the remaining directions.
S takes the last remaining seat, position 3. From clue 7, T's neighbors (Q at 7 and W at 5) face opposite directions. Since Q faces the center, W must face outward. We now have exactly four people facing the center: U, P, Q, and V. Therefore, the remaining four (R, S, T, and W) must face outward.
Completing the arrangement and satisfying the global condition of 4 center-facing and 4 outward-facing individuals.

Key Concept

Advanced Seating Arrangement with Mixed Facing Directions
Estimated Time:2m 30s
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Topics

Seating Arrangement

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