Circular Table Seating Puzzle Explained

This problem involves arranging seven people (A, B, C, D, P, Q, R) around a circular table, with everyone facing the center. The goal is to use the provided clues about their relative positions to figure out the exact seating arrangement and answer the question: Who sits fourth to the right of C?

Understanding Left and Right Directions

When individuals are seated at a circular table facing the center, their left and right directions are relative to their own perspective. For consistency in solving these puzzles:

• Immediate Left is typically considered the position clockwise from the reference person.
• Immediate Right is typically considered the position counter-clockwise from the reference person.
• "Second to the left" means two steps clockwise.
• "Third to the left" means three steps clockwise.
• Similarly, "fourth to the right" means four steps counter-clockwise.

Deducing the Seating Arrangement

We'll number the seats 1 through 7 in a clockwise direction around the table to help track the positions.

1. Clue Analysis: Let's break down the clues:
   • A is immediately to the left of R. (R -> A, clockwise)
   • B is immediately to the left of D. (D -> B, clockwise)
   • D is second to the left of Q. (Q -> Person1 -> D, clockwise)
   • P is third to the left of R. (R -> Person1 -> Person2 -> P, clockwise)
2. Combining Clues: Clues 3 and 2 link D, Q, and B together. The sequence must be Q, followed by one unnamed person, then D, then B immediately after D, all in clockwise order. This forms a block: Q -> X -> D -> B. This block requires 4 consecutive seats.
3. Combining More Clues: Clues 1 and 4 link R, A, and P. A is right after R (R -> A, clockwise). P is three steps clockwise from R (R -> X -> Y -> P, clockwise).
4. Placement Strategy: Let's try placing the 4-person block (Q -> X -> D -> B) first. Assume Q is at Seat 1.
   • Q = Seat 1
   • The next person clockwise is Seat 2.
   • D is second to the left (clockwise) of Q, so D = Seat 3.
   • B is immediately to the left (clockwise) of D, so B = Seat 4.
   • Current partial arrangement (clockwise): Q(1), _(2), D(3), B(4)
5. Placing Remaining People: The remaining seats are 5, 6, and 7. The remaining people are A, C, P, and R. We must fit A, P, and R according to their clues (R -> A clockwise, and R -> X -> Y -> P clockwise).
   • Let's test placing R in the remaining seats (5, 6, 7).
   • If R = Seat 5: A must be Seat 6 (R -> A). P must be third left of R(5). Moving clockwise: R(5) -> A(6) -> Seat 7 -> Seat 1(Q). P would need to be in Seat 1, but Q is already there. This placement doesn't work.
   • If R = Seat 6: A must be Seat 7 (R -> A). P must be third left of R(6). Moving clockwise: R(6) -> A(7) -> Seat 1(Q) -> Seat 2. P should be in Seat 2. This works!
   • So, R=6, A=7, and P=2.
   • The only remaining person is C, and the only remaining seat is 5. So, C = Seat 5.
6. Final Arrangement: Listing the people clockwise starting from Seat 1:

   Q (1), P (2), D (3), B (4), C (5), R (6), A (7)

Verification of Seating Arrangement

Let's confirm if this arrangement satisfies all the initial clues:

• A sits to the immediate left of R? R is at 6, A is at 7 (clockwise). Yes.
• B sits to the immediate left of D? D is at 3, B is at 4 (clockwise). Yes.
• D sits second to the left of Q? Q is at 1. Clockwise: Seat 2 (P) is first left, Seat 3 (D) is second left. Yes.
• P sits third to the left of R? R is at 6. Clockwise: Seat 7 (A) is first left, Seat 1 (Q) is second left, Seat 2 (P) is third left. Yes.

The arrangement is correct.

Answering the Question

The question asks: Who sits fourth to the right of C?

• Find C in the arrangement: C is at Seat 5.
• Move four positions to the right (counter-clockwise).
• 1st right of C(5): Seat 4 (B)
• 2nd right of C(5): Seat 3 (D)
• 3rd right of C(5): Seat 2 (P)
• 4th right of C(5): Seat 1 (Q)

Therefore, Q sits fourth to the right of C.