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.
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How many people sit between R and V?
