A, B, C, D, P, Q and R are sitting around a circular table facing the centre of the table. Only C sits between D and R. R sits third to the left of P. A sits to the immediate left of P. B is not an immediate neighbour of R. Who sits third to the left of Q?
Circular Table Arrangement Logic Puzzle Explained
This problem involves deductive reasoning to determine the seating arrangement of seven people (A, B, C, D, P, Q, R) around a circular table, facing the center, based on a set of clues.
Analyzing Seating Arrangement Clues
Let's break down the clues step-by-step to figure out who sits where. We'll assume positions are numbered 1 to 7 clockwise around the table, and "left" refers to the clockwise direction since they are facing the center.
- People: A, B, C, D, P, Q, R (7 people)
- Setting: Circular table, facing the center.
- Clue 1: 'A sits to the immediate left of P.' This means A is directly clockwise to P. We can represent this as a block: (P -> A)
- Clue 2: 'R sits third to the left of P.' This means counting three positions clockwise from P lands us on R. Combining with Clue 1, if P is at position 1, A is at position 2, the next position (3) is empty, and R is at position 4. The partial arrangement looks like: P, A, __, R, __, __, __ (clockwise).
- Clue 3: 'Only C sits between D and R.' This implies a block of either (D - C - R) or (R - C - D).
- Clue 4: 'B is not an immediate neighbour of R.' B cannot sit in the seat immediately to the left or right of R.
Determining the Seating Order
Let's combine the clues and the partial arrangement (P, A, __, R, __, __, __):
- From Clue 3, we need either D-C-R or R-C-D. Since R is already placed relative to P and A, let's see where D and C fit.
- Consider the R-C-D block. With R at position 4, C must be at position 5 (the next seat clockwise) and D must be at position 6. This fits the structure P(1), A(2), __ (3), R(4), C(5), D(6), __ (7).
- The remaining people are B and Q. The remaining seats are 3 and 7.
- Now apply Clue 4: 'B is not an immediate neighbour of R.' R is at position 4. Its neighbours are position 3 and position 5. C is already at position 5. Therefore, B cannot sit at position 3.
- This means B must sit at the only remaining available position for B, which is position 7.
- Consequently, Q must sit in the last available seat, which is position 3.
- The final clockwise seating arrangement is: P, A, Q, R, C, D, B.
Verifying the Arrangement
Let's double-check if this arrangement satisfies all the conditions:
- C between D and R: Yes (R, C, D sequence is present).
- R third to left of P: P is at 1. 1st left = A (2), 2nd left = Q (3), 3rd left = R (4). Yes.
- A immediate left of P: Yes (P is at 1, A is at 2).
- B not neighbour of R: R is at 4. Neighbours are Q (3) and C (5). B is at 7. Yes.
- All conditions are met.
Finding Who Sits Third to the Left of Q
The question asks who sits third to the left (clockwise) of Q.
- Q is at position 3 in our arrangement (P, A, Q, R, C, D, B).
- The first person to the left (clockwise) of Q is R (position 4).
- The second person to the left (clockwise) of Q is C (position 5).
- The third person to the left (clockwise) of Q is D (position 6).
Therefore, D sits third to the left of Q.
Important Questions from Seating Arrangement (Notes)
- Five friends are sitting on a bench in the following order :
(i) P is sitting next to Q and R is next to S.
(ii) S is not sitting with T; T is on the extreme left hand side of the bench and R is on second position from the right hand side.
(iii) P is on the right hand side of Q and to the right side of T. (iv) P and R sitting together
Who is sitting exactly in the middle ? Seven people, C, D, E, F, L, M and N, are sitting in a row, facing north.
Only two people sit to the right of C. Only two people sit between C and L. Only two people sit between E and N. N sits to the immediate left of C. M sits to the immediate right of F. Who sits at the third position from the left end of the row?- Seven people, A, B, C, D, E, F and G, are sitting in a row, facing north. Only three people sit between E and D. A sits to the immediate left of D. No one sits to the right of B. Only two people sit between B and A. G sits to the immediate right of F. How many people sit to the right of F?
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?
