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
Eight friends, A, B, C, D, E, F, G and H, are sitting in two lines of four persons each. Both the lines are facing each other. A is facing D. E is to the immediate left of G. H is to the immediate right of B. C is facing G. F is facing H. B is to the immediate right of the person who is facing G. D is to the immediate left of F. Which four persons are sitting in the same line?
Nine employees, K, L, M, N, O, P, Q, R and S, are sitting in the office in a straight line, all facing the east. O is third to the right of M. K is third to the left of P. Q is between P and S. N is fourth to the right of M. P is to the immediate right of N. R is fourth to the left of O. Which of the following statements is NOT correct?
Eight north-facing restaurants named P, Q, R, S, T, U, V and W are located in a straight line. S is second to the left of T. W is third to the left of P. T is between P and V. S is third to the left of V. W is to the immediate right of U. R is third to the right of P. Who is sitting fourth to the right of S?
Anamika, Gopal, Nischal, Vanmayi, Shresta and Sripad are sitting in a straight line facing the north. Nischal is to the immediate left of Gopal. Shresta is between Anamika and Sripad. Sripad is at the second place from the right end. Four persons are sitting between Nischal and Vanmayi. If Gopal and Sripad interchange their positions, then who will be sitting between Vanmayi and Shresta?
A question is given, followed by two statements numbered (I) and (II). You have to decide whether the data provided in the statements is sufficient to answer the question. Read both the statements and select the appropriate answer.
Question: How many people are standing in the row where all people are facing north?
Statements:
(I) A is fourth from the left end; M is second to the right of A; and R is second from the left end.
(II) M is fourth from the right end; only two people Stand between M and B.
