6 persons A, B, C, D, E and F are sitting around a rectangular table, facing towards the centre (not necessarily in the same order). One person is sitting on each of the smaller sides. Two persons are sitting on each of the bigger sides. No person is sitting at the corners. C and F are sitting on the same side. B is sitting opposite to A. F is the immediate neighbour of B. A is sitting second to the left of D. Counting towards the left of D, how many persons are sitting between A and D?
One
Rectangular Table Seating Arrangement Puzzle Solution
This problem presents a seating arrangement puzzle involving six persons (A, B, C, D, E, F) around a rectangular table. They are all facing the center. The table has a specific layout: one person sits on each of the two shorter sides, and two persons sit on each of the two longer sides. No one is sitting at the corners. Our goal is to determine the exact seating positions of all six individuals by carefully analyzing the given clues and then answer the final question about the number of persons between A and D.
Table Layout Understanding
Let's define the six positions around the rectangular table. A standard representation for such a table, where everyone faces the center, would have positions arranged as follows (moving clockwise from the top-left):
- P1: Top-Left (Long Side)
- P2: Top-Right (Long Side)
- P3: Middle-Right (Short Side)
- P4: Bottom-Right (Long Side)
- P5: Bottom-Left (Long Side)
- P6: Middle-Left (Short Side)
This setup ensures two persons on each long side (P1 & P2; P4 & P5) and one person on each short side (P3; P6), totaling six persons, matching the problem description.
Analyzing Seating Clues Step-by-Step
We will deduce the seating arrangement by breaking down each clue provided:
Clue 1: Persons C and F are sitting on the same side.
- Since each shorter side (P3 or P6) can only accommodate one person, C and F must be seated on one of the longer sides. This means they occupy either positions (P1, P2) or (P4, P5).
Clue 2: Person B is sitting opposite to person A.
- In a rectangular table with this configuration, the persons directly opposite each other are those on the shorter sides.
- Therefore, B and A must be occupying the positions P3 and P6 (the two shorter sides).
Clue 3: Person F is the immediate neighbour of person B.
- From Clue 1, F is on a longer side. From Clue 2, B is on a shorter side.
- Let's consider two possibilities for B's position:
- Possibility A: Assume B is at P3 (Middle-Right short side).
- The immediate neighbours of P3 (facing center) are P2 (Top-Right) and P4 (Bottom-Right).
- If F is an immediate neighbour of B, F must be either at P2 or P4.
- If F is at P2 (Top-Right), then from Clue 1 (C and F on the same side), C must be at P1 (Top-Left).
- So far, we have: P1 → C, P2 → F, P3 → B.
- Since B is at P3, and B is opposite A (Clue 2), A must be at P6 (Middle-Left short side).
- Current placement: P1 → C, P2 → F, P3 → B, P6 → A.
- The remaining persons are D and E, and the remaining positions are P4 and P5 (the bottom long side).
- Possibility B: Assume B is at P6 (Middle-Left short side).
- The immediate neighbours of P6 (facing center) are P1 (Top-Left) and P5 (Bottom-Left).
- If F is an immediate neighbour of B, F must be either at P1 or P5.
- If F is at P1 (Top-Left), then from Clue 1, C must be at P2 (Top-Right).
- So far, we have: P6 → B, P1 → F, P2 → C.
- Since B is at P6, A must be at P3.
- Current placement: P6 → B, P1 → F, P2 → C, P3 → A.
- Remaining persons D and E for positions P4 and P5.
- Possibility A: Assume B is at P3 (Middle-Right short side).
Clue 4: Person A is sitting second to the left of person D.
We will use this final clue to confirm the correct possibility from Clue 3.
- Continuing with Possibility A (A at P6):
- A is at P6. D must be at either P4 or P5.
- Let's determine left/right movement from P4 and P5 (facing center):
- From P4 (Bottom-Right): 1st left is P5; 2nd left is P6.
- From P5 (Bottom-Left): 1st left is P4; 2nd left is P3.
- If D is at P4: Second to D's left is P6. Since A is at P6, this matches the clue!
- This confirms that D is at P4.
- Consequently, E, the last remaining person, must be at P5.
- If we tried Possibility B (A at P3):
- A is at P3. D must be at either P4 or P5.
- From P4 (Bottom-Right): 1st left is P5; 2nd left is P6. (A is not at P6)
- From P5 (Bottom-Left): 1st left is P4; 2nd left is P3. (A is at P3).
- This would mean D is at P5. Let's check consistency. If D is at P5, F must be at P1 or P5. If F is at P5 and D is at P5, this is not possible. So Possibility B does not lead to a consistent solution.
Final Seating Arrangement
Based on our deductions, the only consistent arrangement is:
| Position | Person | Side Type |
|---|---|---|
| P1 | C | Top Long Side |
| P2 | F | Top Long Side |
| P3 | B | Right Short Side |
| P4 | D | Bottom Long Side |
| P5 | E | Bottom Long Side |
| P6 | A | Left Short Side |
Let's quickly verify all original conditions with this final arrangement:
- C (P1) and F (P2) are on the same side (Top Long Side). (Satisfied)
- B (P3) is sitting opposite to A (P6). (Satisfied)
- F (P2) is the immediate neighbour of B (P3). (Satisfied)
- A (P6) is sitting second to the left of D (P4). From D (P4), 1st left is E (P5), 2nd left is A (P6). (Satisfied)
All conditions are met by this arrangement.
Counting Persons Between A and D (Counting Left from D)
The question asks: Counting towards the left of D, how many persons are sitting between A and D?
- D is at position P4.
- A is at position P6.
- Let's trace the path by moving left from D (P4):
- The person immediately to the left of D (P4) is E (at P5).
- Moving further left, the next person is A (at P6).
Therefore, when counting towards the left of D, person E is the only individual sitting between D and A.
Thus, there is One person sitting between A and D.
Important Questions from Polygon Arrangement
A, B, C, D, E, F, G and H are sitting around a square table facing the centre of the table. Some of them are sitting at the corners while some are sitting at the exact centre of the sides.
G sits second to the right of F. B sits second to the right of A. C sits third to the right of H. E sits third to the right of F. C is not the immediate neighbour of A. Who sits second to the right of B?
Seven friends, A, B, C, D, E, F, and G are seating around a square table, facing towards the centre. Some of them are sitting at the corners while some are sitting at the exact centre of the sides of the table. One seat is left vacant. D is sitting exactly at the centre of one of the sides of the table. C is sitting at a corner, third to the left of B. There are exactly two people sitting between C and D. F is an immediate neighbour of both B and D. A is second to the right of F. E is not an immediate neighbour of A, but third to the left of F. G is an immediate neighbour of C. Where is the vacant seat?
Rashmi, Sunita, Mona and Sakshi are sitting around a square table. Rashmi is to the right of Sunita. Mona is to the left of Sakshi. Which of the persons mentioned in the options is sitting opposite to each other?
V, W, X, Y, Z, A, B and C were sitting around a square table facing the centre. Some of these were sitting at corners and some were sitting at exact centre of the sides. C was to the immediate right of W. B was third to the left of Z. A was the immediate neighbour of X and C. Z, not at any corner, was the immediate neighbour of W and Y. Who among the following was sitting third to the right of A?
8 boys G, H, I, J, K, L, M and N are sitting around a square table facing towards the centre (not necessarily in the same order). Four boys are sitting at the corner and four boys are sitting in the middle of the sides. J is the immediate neighbour of G and H and he is sitting at a corner. M is the immediate neighbour of N and K. L is the sitting in the middle of the side. G is not sitting opposite to L. N is towards the immediate right of H.
Who is sitting diagonally opposite to I?
