Seven people I, Y, O, U, R, P, and T are sitting in a straight row, facing north. P sits at the extreme right. Only six people sit to the right of R. Y sits fourth to the left of P. T is the immediate neighbour of R. I sits fourth to the right of R. U and T are the immediate neighbours of Y. O is the immediate neighbour of P. Who sits at the centre of the row?
U
Understanding the Seating Arrangement Puzzle
This question asks us to determine who is sitting in the centre of a row of seven people based on a series of clues about their relative positions. The people are I, Y, O, U, R, P, and T, and they are all facing North.
Step-by-Step Deduction of Seating Positions
Let's break down the clues and place the people in the row. There are seven positions in the row, which we can number 1 through 7 from left to right since they are facing North.
- P sits at the extreme right. The extreme right position is position 7. So, P is at position 7.
- Only six people sit to the right of R. For six people to be to the right of R, R must be at the first position from the left (position 1). If R is at position 1, then positions 2, 3, 4, 5, 6, and 7 are to the right of R, which is exactly six people.
- Y sits fourth to the left of P. P is at position 7. Moving four positions to the left from position 7 brings us to position $7 - 4 = 3$. So, Y is at position 3.
- T is the immediate neighbour of R. R is at position 1. Its only immediate neighbour in the row is position 2. So, T is at position 2.
- I sits fourth to the right of R. R is at position 1. Moving four positions to the right from position 1 brings us to position $1 + 4 = 5$. So, I is at position 5.
- U and T are the immediate neighbours of Y. Y is at position 3. Its immediate neighbours are at positions 2 and 4. We already know T is at position 2. Therefore, U must be at position 4.
- O is the immediate neighbour of P. P is at position 7. Its only immediate neighbour in the row is position 6. So, O is at position 6.
Consolidated Seating Arrangement
Based on the steps above, we can fill the positions from 1 to 7:
Position 1: R
Position 2: T
Position 3: Y
Position 4: U
Position 5: I
Position 6: O
Position 7: P
The complete arrangement from left to right is:
R T Y U I O P
Identifying the Centre of the Row
The row has 7 people. To find the centre position in a row of an odd number of people, you can use the formula $\frac{n+1}{2}$, where $n$ is the number of people. In this case, $n=7$.
Centre position = $\frac{7+1}{2} = \frac{8}{2} = 4$th position.
Looking at our arrangement R T Y U I O P, the person at the 4th position is U.
Verification
Let's quickly check if all conditions are met with the arrangement R T Y U I O P:
- P sits at extreme right (Position 7) - Yes.
- Only six people sit to the right of R (Positions 2-7 are right of R) - Yes.
- Y sits fourth to the left of P (P at 7, Y at 3; $7-4=3$) - Yes.
- T is immediate neighbour of R (T at 2, R at 1) - Yes.
- I sits fourth to the right of R (R at 1, I at 5; $1+4=5$) - Yes.
- U and T are immediate neighbours of Y (Y at 3, T at 2, U at 4) - Yes.
- O is immediate neighbour of P (O at 6, P at 7) - Yes.
All conditions are satisfied by the arrangement R T Y U I O P.
The person sitting at the centre of the row (4th position) is U.
| Position (Left to Right) | Person |
|---|---|
| 1 | R |
| 2 | T |
| 3 | Y |
| 4 (Centre) | U |
| 5 | I |
| 6 | O |
| 7 | P |
Revision Table: Seating Arrangement Key Clues
| Clue | Deduction | Current Arrangement |
|---|---|---|
| 7 people, row, North | Positions 1 to 7 | _ _ _ _ _ _ _ |
| P sits extreme right | P at Pos 7 | _ _ _ _ _ _ P |
| 6 people right of R | R at Pos 1 | R _ _ _ _ _ P |
| Y fourth left of P | Y at Pos $7-4=3$ | R _ Y _ _ _ P |
| T immediate neighbour of R | T at Pos 2 | R T Y _ _ _ P |
| I fourth right of R | I at Pos $1+4=5$ | R T Y _ I _ P |
| U and T immediate neighbours of Y | U at Pos 4 (T is already at Pos 2) | R T Y U I _ P |
| O immediate neighbour of P | O at Pos 6 | R T Y U I O P |
Additional Information: Linear Seating Arrangement Concepts
Linear seating arrangement problems involve arranging people or objects in a single line based on given conditions. Key concepts include:
- Understanding Direction: Facing North typically means Left is on the left side of the paper/screen and Right is on the right side. Facing South reverses this.
- Relative Positions: Clues like "left of," "right of," "immediate neighbour," "second to the left," "fourth to the right" are common. "Nth to the left/right of X" means there are N-1 people between X and the person being placed.
- Extreme Ends: "Extreme left" and "extreme right" refer to the first and last positions in the row.
- Neighbours: Immediate neighbours are the people directly next to someone on either side.
- Centre Position: In a row of N people, the centre position is $\frac{N+1}{2}$ if N is odd. If N is even, there are two centre positions, N/2 and (N/2)+1.
- Building the Arrangement: Start with the most definitive clues (like extreme positions) and then use relative position clues to fill in the gaps.
- Verification: Always check the final arrangement against all the given conditions to ensure accuracy.
Important Questions from Linear Arrangement
M, N, L, O, Q and H are sitting in a row. Q and H are in the centre. M and N are at the ends. L is sitting to the immediate left of N. Who is to the right of M?
Five friends, Shruti, Shreya, Anup, Ankit and Kiran, are sitting in a row facing towards the south. Shruti is between Shreya and Anup. Kiran and Shreya are sitting at the extreme ends of the west and east, respectively. Who is sitting in the middle?
Five students are standing in a line. Suman is standing next to Pranav but not next to Deena. Kumar is standing next to Raju, who is standing on the extreme left, and Deena is not standing next to Kumar.
Who is standing in the middle?Eight friends, A, B, C, D, E, F, G and H, are sitting in a straight line, all facing the north. F is sitting between D and G. B is sitting between H and A. E is third to the left of G. G is sitting at one of the corners. H is third to the left of C. Who is sitting between A and E?
Five students are sitting in a row. Akbar is to the left of the person sitting in the middle, but to the right of Sekar. Prakash is to the right of Deva, and Ram is to the right of Prakash. Ram is second from the person sitting in the middle. Who is the person sitting in the middle?
