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.
- 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)
- 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.
- 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).
- 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)
- 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.
- 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.
Important Questions from Seating Arrangement (Notes)
Read the directions carefully and give the answer from the given options.
P, Q, R, S, T, K, L, M and N are sitting around a circle facing the centre.
K is $4^{th}$ to the right of P and P is $3^{rd}$ to the right of Q.
N is $4^{th}$ to the left of Q and $3^{rd}$ to the right of S.
R is $2^{nd}$ to the right of M and M is the immediate neighbour of P.
T is $2^{nd}$ to the left of L.
Who is to the immediate left of K?
Seven people, F, J, M, L, R, V and X, are sitting in a row, facing north.
Only three people sit to the left of X. Only M sits to the right of R. Only three people sit between R and V. J sits at some place to the left of L but at some place to the right of F.
How many people sit to the left of V?Seven boxes, A, B, C, D, E, F and G, are kept one over the other but not necessarily in the same order. Only A is kept above F. Only D is kept between F and C. Only E is kept below B. How many boxes are kept below C?
P, Q, R, S, T, U and V are sitting in a row, facing north. No one sits to the left of U. Only four people sit between U and R. Only three people sit to the right of V. P sits to the immediate left of S. Q is not an immediate neighbour of V. How many people sit between P and T?
Six people, B, C, D, I, J and K, are sitting around a circular table facing the centre. Only two people sit between B and I when counted from the right of I. K sits to the immediate left of J. I sits to the immediate right of C. Who among the following are the immediate neighbours of D?
