Seven persons are sitting around a circular dining table facing the towards the centre. S is sitting to the immediate left of Y and third to the right of R. R is sitting to the immediate left of A and immediate right of P. A is sitting to the immediate left of D. Q is sitting to the immediate left of P. If D exchanges seat with Y and P with Q, then who is sitting to the immediate right of D?
P
This solution explains the step-by-step process to determine the seating arrangement around a circular table based on the given clues and identify the person sitting to the immediate right of D after a seat exchange.
Understanding the Seating Arrangement Problem
We are given clues about the relative positions of seven people (A, D, P, Q, R, S, Y) sitting around a circular table facing the center. We need to find the final arrangement after specific seat exchanges.
Determining the Initial Seating Arrangement
Let's break down the clues to establish the initial order:
- Clue 5 & 7: "R is sitting to the immediate right of P" and "Q is sitting to the immediate left of P". This gives us a block: Q is to P's left, and R is to P's right. Since they face the center, left/right refers to the arrangement from a top-down view, going counter-clockwise for left and clockwise for right, or vice-versa consistently. Let's assume clockwise is right. So, P is to the left of R, and Q is to the left of P. Sequence: Q - P - R.
- Clue 4: "R is sitting to the immediate left of A". This extends the sequence: Q - P - R - A.
- Clue 6: "A is sitting to the immediate left of D". This further extends the sequence: Q - P - R - A - D.
- Clue 2: "S is sitting to the immediate left of Y". This gives us another block: S - Y.
- Clue 3: "S is sitting [...] third to the right of R". Let's use the sequence Q - P - R - A - D. We need to place S and Y. R has A to its right (1st), D to its right (2nd). The third person to R's right must be S. So, the arrangement becomes: R - A - D - S - ? - ? - R (circularly).
- Combining the blocks: We have Q - P - R - A - D. And we know S is third to R's right. The sequence is R, A (1st right), D (2nd right), S (3rd right). This fits perfectly if S is placed after D. Now we need to place Y.
- Using Clue 2 again: "S is sitting to the immediate left of Y". This means Y must be immediately to the right of S.
- Fitting everything together circularly (clockwise): Start with P. R is to the right of P (Clue 5). Q is to the left of P (Clue 7). So we have Q P R. A is to the right of R (Clue 4). D is to the right of A (Clue 6). So we have Q P R A D. S is third to the right of R (Clue 3): R -> A (1st) -> D (2nd) -> S (3rd). So the order continues R A D S. Y is to the right of S (Clue 2). So we have Q P R A D S Y. This completes the circle of 7 people.
Initial Arrangement (Clockwise): P, R, A, D, S, Y, Q.
Let's verify:
- S left of Y? Yes (Y is clockwise to S).
- S third right of R? R -> A (1st) -> D (2nd) -> S (3rd). Yes.
- R left of A? Yes.
- R right of P? Yes.
- A left of D? Yes.
- Q left of P? Yes.
The initial clockwise order is confirmed as: P, R, A, D, S, Y, Q.
Performing the Seat Exchange
The specified exchanges are:
- D exchanges seat with Y.
- P exchanges seat with Q.
Applying these exchanges to the initial clockwise arrangement (P, R, A, D, S, Y, Q):
- Original positions:
- Seat 1: P
- Seat 2: R
- Seat 3: A
- Seat 4: D
- Seat 5: S
- Seat 6: Y
- Seat 7: Q
- After D swaps with Y:
- Seat 1: P
- Seat 2: R
- Seat 3: A
- Seat 4: Y (was D)
- Seat 5: S
- Seat 6: D (was Y)
- Seat 7: Q
- After P swaps with Q:
- Seat 1: Q (was P)
- Seat 2: R
- Seat 3: A
- Seat 4: Y
- Seat 5: S
- Seat 6: D
- Seat 7: P (was Q)
New Arrangement (Clockwise): Q, R, A, Y, S, D, P.
Identifying Who is to the Immediate Right of D
In the new clockwise arrangement (Q, R, A, Y, S, D, P):
- Find D in the sequence.
- The person immediately following D in the clockwise direction is the person to D's immediate right.
- The sequence around D is S - D - P.
- Therefore, P is sitting to the immediate right of D.
Final Answer Calculation
The initial arrangement derived from the clues is P, R, A, D, S, Y, Q (clockwise).
After swapping D with Y and P with Q, the new clockwise arrangement is Q, R, A, Y, S, D, P.
Observing the new arrangement, the person seated immediately to the right (clockwise) of D is P.
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