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Difficulty: Very hardSeating Arrangement

Eight colleagues—P, Q, R, S, T, U, V, and W—are sitting around a circular table, representing eight different departments: HR, IT, Sales, Legal, Marketing, Operations, R&D, and Finance, though not necessarily in that exact order.

Four of them face the center of the table and four face outside. Not more than two adjacent persons face the same direction.

Read the following information carefully:
• P is from HR, faces the center, and sits opposite T, who is from Marketing.
• The Sales representative sits second to the left of P.
• R is from Sales and sits exactly between the Legal representative and Q.
• Q sits immediately to the left of P.
• The person from Legal faces the same direction as P, but opposite to that of R.
• The IT representative sits third to the left of the Legal representative.
• U is from Operations and sits immediately to the right of T, who faces outside.
• W sits opposite the Legal representative and faces the same direction as U.
• V sits immediately to the left of W.
• The Finance representative sits exactly between V and P.

Which of the following statements are correct? (Select all that apply)

  1. V sits third to the left of S and represents the IT department.Answer
  2. B
    The representative from R&D faces the center and sits immediately to the right of the Sales representative.
  3. W and R face the same direction, and both have only center-facing immediate neighbors.Answer
  4. D
    The Operations representative faces outside and sits second to the right of the Legal representative.

Answer

The statements verifying that V sits third to the left of S representing IT, and that W and R face the same direction surrounded by center-facing neighbors, are correct.
Based on the fully deduced arrangement, S (Legal) is at position 4 facing the center. Counting three places to the left (clockwise) lands on position 7, which is V (IT). Furthermore, W and R both face outside, and examining their immediate neighbors confirms that all four adjacent individuals (V, P, Q, S) face the center.

Step-by-Step Solution

1
Place P and T, and determine left/right paths.
Assign positions 1 to 8 clockwise. Let P be at position 1 (HR, faces Center). T is opposite at position 5 (Marketing).
Establishing a numerical clockwise perimeter anchors relative directions. For center-facing people, left is clockwise (+). For outside-facing people, left is counter-clockwise (-).
2
Place Q, R, and identify Legal.
Q is immediate left of P(1, Center) -> Q is at 2. Sales is 2nd left of P -> Sales is at 3, so R is at 3. Since R is between Legal and Q(2), Legal must be at 4. The only unmentioned person, S, is Legal.
Sequential placement using P's center-facing orientation locks the entire left side of the table.
3
Determine directions for Legal and Sales, then place IT.
Legal(4) faces Center (same as P). R(3) faces Outside (opposite of P). IT is 3rd left of Legal(4, Center) -> 4 + 3 = 7. So IT is at 7.
Applying the relative direction rules based on the explicitly stated facing orientations.
4
Place U (Ops) and W (Finance).
T(5) faces Outside. Immediate right is clockwise (+) -> 5 + 1 = 6. U(Ops) is at 6. W is opposite Legal(4) -> W is at 8. Finance is between V and P(1). W(8) is between 7 and 1, so W is Finance.
Filling the remaining departmental gaps and using opposite constraints locks the physical locations.
5
Determine V's position and the remaining facing directions.
V is at 7 (IT). V is immediate left of W(8). Since 7 is counter-clockwise from 8, W must face Outside. W and U face the same direction, so U(6) faces Outside. Known directions: P(C), R(O), S(C), T(O), U(O), W(O).
Using the definition of 'left' to reverse-engineer W's facing direction.
6
Apply global constraints to finalize directions and assignments.
We need exactly 4 Center and 4 Outside. We have four Outside (R, T, U, W). Therefore, the remaining two (Q at 2, V at 7) MUST face the Center. This also satisfies the rule of max two adjacent people facing the same direction. Q takes the last department, R&D.
Global constraints cross-verify the layout and lock the final unknown variables.

Key Concept

Solving complex multi-variable seating arrangements by cross-referencing relative directional rules (left/right) with dynamic inward/outward facing orientations.
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Topics

Seating Arrangement

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