Seven people, A, B, C, D, E, F and G, are sitting in a straight row facing the north. Only two people sit to the left of C. Only two people sit between A and B. B sits to the left of A. E is an immediate neighbour of A to the right. Only one person sits to the right of D. F is not an immediate neighbour of B. Who sits at the centre?
A
Understanding the Seating Arrangement Puzzle
This question asks us to determine the exact seating order of seven people (A, B, C, D, E, F, and G) sitting in a straight row facing North. We are given several clues that restrict their possible positions. By carefully analyzing each clue and combining the information, we can deduce the final arrangement and identify the person sitting in the center.
Step-by-Step Deduction of the Seating Order
Let's represent the seven seats in the straight row facing North. Since they face North, their left is our left, and their right is our right.
The seats can be numbered 1 to 7 from left to right:
Seat 1 - Seat 2 - Seat 3 - Seat 4 - Seat 5 - Seat 6 - Seat 7
Now, let's process the clues:
- Clue 1: Only two people sit to the left of C.
This directly tells us C's position. If two people are to the left of C, C must be in the 3rd seat from the left.
Arrangement so far: \_ \_ C \_ \_ \_ \_
Seats: 1 2 3 4 5 6 7 - Clue 2: Only one person sits to the right of D.
If only one person is to the right of D, D must be in the 6th seat from the left.
Combining with Clue 1: \_ \_ C \_ \_ D \_
Seats: 1 2 3 4 5 6 7 - Clue 3: Only two people sit between A and B. B sits to the left of A. This gives us a block pattern: B \_ \_ A. B is to the left of A.
- Clue 4: E is an immediate neighbour of A to the right. This gives us a block pattern: A E.
Now, let's try to fit the blocks B \_ \_ A and A E into the arrangement \_ \_ C \_ \_ D \_. The available seats are 1, 2, 4, 5, and 7.
- The block A E requires two adjacent seats. The possible pairs are (4, 5), (5, 6), (6, 7).
- Seat 6 is occupied by D. So, A E can be in seats (4, 5) or (6, 7).
- If A E are in seats (6, 7), A is at 6 and E is at 7. But seat 6 is D. This is not possible.
- Therefore, A E must be in seats (4, 5). A is at seat 4, and E is at seat 5.
Updated arrangement: \_ \_ C A E D \_
Seats: 1 2 3 4 5 6 7
Now fit the block B \_ \_ A (B is left of A). A is at seat 4. Two seats must be between B and A, and B must be to A's left.
- Counting two seats to the left of A (seat 4) means we look at seat 3 and seat 2. B must be one seat to the left of seat 2.
- Seat 3 is occupied by C. Seat 2 is empty. Seat 1 is empty.
- If B \_ \_ A is B at seat 1, then seat 2 and seat 3 are between B and A (at seat 4). The arrangement B \_ C A fits the pattern B \_ \_ A.
- So, B is at seat 1.
Updated arrangement: B \_ C A E D \_
Seats: 1 2 3 4 5 6 7
The people placed so far are B, C, A, E, D. The remaining people are F and G. The remaining empty seats are 2 and 7.
The arrangement is currently: B (F/G) C A E D (F/G)
- Clue 5: F is not an immediate neighbour of B. B is at seat 1. The immediate neighbour of B is the person at seat 2. Therefore, F cannot be at seat 2.
Since seat 2 must be either F or G, and F cannot be at seat 2, G must be at seat 2.
If G is at seat 2, the only remaining person is F, and the only remaining seat is 7. So, F must be at seat 7.
Final Seating Arrangement
The final seating arrangement from left to right is:
B G C A E D F
Seats: 1 2 3 4 5 6 7
Identifying the Person in the Center
There are 7 people. The center position in a row of 7 is the 4th position (since $(7+1)/2 = 4$).
Looking at the final arrangement, the person in the 4th seat is A.
Therefore, A sits at the centre.
| Clue | Deduction | Partial/Final Arrangement (Seats 1-7) |
|---|---|---|
| Only two people left of C | C is at Seat 3 | \_ \_ C \_ \_ \_ \_ |
| Only one person right of D | D is at Seat 6 | \_ \_ \_ \_ \_ D \_ |
| Combining C and D | C at 3, D at 6 | \_ \_ C \_ \_ D \_ |
| B _ _ A (B left of A), A E (E right of A) | A E must be seats 4-5, B must be seat 1 | B \_ C A E D \_ |
| Remaining people F, G; Remaining seats 2, 7 | B (F/G) C A E D (F/G) | |
| F is not neighbour of B | F is not at Seat 2 | G is at Seat 2, F is at Seat 7 |
| Final Arrangement | B G C A E D F |
Revision Table: Key Positions
| Seat Number | Person |
|---|---|
| 1 | B |
| 2 | G |
| 3 | C |
| 4 (Center) | A |
| 5 | E |
| 6 | D |
| 7 | F |
Additional Information: Solving Seating Puzzles
Seating arrangement puzzles are common in logical reasoning sections of various exams. Here are some tips for solving them effectively:
- Read all clues carefully before starting.
- Identify the most restrictive clues first (e.g., fixed positions like ends or specific numbered spots, or definite neighbours).
- Use diagrams or draw the seats to visualize the arrangement.
- Represent uncertain positions or possibilities (like F/G) and eliminate them as more clues are used.
- Break down complex clues into smaller pieces (e.g., "B sits to the left of A" and "two people sit between A and B" together mean B \_ \_ A).
- Cross-check your final arrangement against all given clues to ensure consistency.
- For a row of N people, the center position is at $(N+1)/2$ if N is odd.
Important Questions from Linear Arrangement
P, Q, R and S are sitting on a bench and facing in the same direction. P sits next to Q but not next to R. S, who is sitting on the extreme right, does not sit next to either Q or R. How many of them each have two neighbors?
Five friends Ram, Priya, Raunak, Aditya and Shyam are sitting in a row facing north. Raunak is to the right of Shyam and Priya is to the left of Shyam but to the right of Rama. Raunak is to the left of Aditya. Who is fourth from the left end?
Six people P, Q, R, S, T and U sit in a row, not necessarily in the same order. If two persons sit in between P and Q, and two persons sit in between T and U, then how many persons sit in between R and S?
Six persons P, Q, R, S, T and U are sitting in a row facing north (not necessarily in the same order). Q sits fourth to the right of S. One person sits between P and Q. Three persons sit between R and T. R sits immediate left of P. How many persons sit between T and U?
Five chairs C01, C02, C03, C04 and C05 are placed one above the other but not necessarily in the same order. If C03 is above C02, C01 is above C05 but below C04 and C05 is above C03, which chair is in the middle?
