Seven friends O, P, Q, R, S, T and U are watching a movie sitting in a row. S is sitting at one extreme end. Q is sitting second to the right of S. P is sitting between O and Q. U is not sitting at any extreme end. O is not at any extreme end. R is sitting immediate left of T. Who is sitting in the middle?
P
Understanding the Seating Arrangement Puzzle
This problem requires us to determine the exact seating order of seven friends (O, P, Q, R, S, T, U) sitting in a single row based on a set of given conditions. By carefully analyzing each condition and deducing possibilities, we can establish the final arrangement and identify the person in the middle.
Step-by-Step Deduction of the Seating Order
Let's break down the given conditions and build the seating arrangement one step at a time for the 7 positions in the row:
- "S is sitting at one extreme end."
This means S is either at the first position from the left or the last position from the right. Let's represent the 7 positions as slots: _ _ _ _ _ _ _ Possibility 1: S _ _ _ _ _ _ Possibility 2: _ _ _ _ _ _ S - "Q is sitting second to the right of S."
If S is at the left extreme (Position 1), Q must be at Position 3 (1 + 2 = 3). S _ Q _ _ _ _ If S were at the right extreme (Position 7), its right side would be beyond the row, so Q cannot be second to its right within the row. Therefore, S must be at the left extreme end (Position 1). Current arrangement: S _ Q _ _ _ _ Positions: 1 2 3 4 5 6 7 - "P is sitting between O and Q."
This implies the three friends O, P, and Q are likely seated in a sequence where P is located in the middle of O and Q. This can be interpreted as a contiguous block like O P Q or Q P O, or simply that P is located in positions between O and Q in the final arrangement. Given the flow of other clues, a contiguous block is a strong possibility. We know Q is at Position 3. If Q P O forms a block starting at Q, P would be at Position 4 and O at Position 5. Let's test this possibility. Current arrangement: S _ Q P O _ _ Positions: 1 2 3 4 5 6 7 - "U is not sitting at any extreme end."
U cannot be at Position 1 or Position 7. - "O is not at any extreme end."
O cannot be at Position 1 or Position 7. In our potential arrangement (S _ Q P O _ _), O is at Position 5, which is not an extreme end. This fits this condition. U must be placed in one of the remaining non-extreme spots. - "R is sitting immediate left of T."
This means R and T must sit together as a block (RT) with R first, then T. The available spots in our potential arrangement (S _ Q P O _ _) are Positions 2, 6, and 7. The only pair of consecutive spots available is Positions 6 and 7. So, R must be at Position 6 and T at Position 7. Arrangement so far: S _ Q P O R T Positions: 1 2 3 4 5 6 7 - Placing the remaining person:
The only person left is U, and the only position left is Position 2. Let's place U there. Final proposed arrangement: S U Q P O R T Positions: 1 2 3 4 5 6 7
Verification of the Final Seating Arrangement
Let's check if this arrangement satisfies all the original conditions:
- Seven friends O, P, Q, R, S, T and U are watching a movie sitting in a row. (Yes - S, U, Q, P, O, R, T are 7 friends in a row).
- S is sitting at one extreme end. (Yes - S is at Position 1).
- Q is sitting second to the right of S. (Yes - Q is at Position 3, which is second to the right of S at Position 1).
- P is sitting between O and Q. (Yes - P is at Position 4, between Q at 3 and O at 5).
- U is not sitting at any extreme end. (Yes - U is at Position 2, not 1 or 7).
- O is not at any extreme end. (Yes - O is at Position 5, not 1 or 7).
- R is sitting immediate left of T. (Yes - R is at Position 6, immediately left of T at Position 7).
All conditions are met by the arrangement S U Q P O R T.
Identifying the Person in the Middle
In a row of 7 people, the middle position is the 4th position.
| Position | Friend |
|---|---|
| 1 | S |
| 2 | U |
| 3 | Q |
| 4 (Middle) | P |
| 5 | O |
| 6 | R |
| 7 | T |
The friend sitting at the 4th position is P.
Revision Table: Key Deductions
| Condition | Deduction | Impact on Arrangement |
|---|---|---|
| S at extreme end | S at Pos 1 or Pos 7 | Limits possibilities for S |
| Q 2nd right of S | S must be at Pos 1, Q at Pos 3 | Fixes S and Q positions early: S _ Q _ _ _ _ |
| P between O and Q | Suggests O P Q or Q P O sequence; QPO fits with Q at Pos 3 | Places P at Pos 4, O at Pos 5: S _ Q P O _ _ |
| U not at extreme | U ≠ Pos 1, 7 | U must be in {2, 4, 5, 6} (later narrowed down) |
| O not at extreme | O ≠ Pos 1, 7 | Confirmed by O at Pos 5 |
| R immediate left of T (RT block) | RT must occupy consecutive spots | Only Pos 6 & 7 are available: S _ Q P O R T |
| Remaining person U, remaining spot Pos 2 | U goes to Pos 2 | Final Arrangement: S U Q P O R T |
Additional Information: Solving Seating Puzzles
Seating arrangement puzzles are common in logical reasoning sections of exams. They test your ability to process multiple conditions simultaneously and build a coherent structure. Here are some tips for solving them:
- Draw a diagram or use placeholders for positions.
- Start with the most restrictive conditions, like those fixing someone at an end or relative positions (e.g., 'immediate left of').
- Look for connections between conditions (e.g., if A is left of B, and B is right of C, it helps link positions).
- Use abbreviations for names.
- Systematically test possibilities if the initial conditions don't immediately fix many positions.
- Always verify your final arrangement against all the given conditions.
- Pay close attention to wording like "immediate left/right" vs. just "left/right" and "between" (which can sometimes imply adjacency, or just being located somewhere in the segment between the two reference points).
Important Questions from Linear Arrangement
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?
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?
5 boys A, B, C, D and E are sitting in a row. E is sitting between D and A, B is to the right of A, C is at one of the extreme ends and C and D are sitting next to each other. Which of the following statement is false?
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?
Seven friends P, Q, R, S, T, U, and V are sitting in a straight line facing north. Q sits fifth to the right of T. Q does not sit at any of the extreme ends. Two people sit between U and R. S sits third to the left of V. S sits exactly in the middle. U is not an immediate neighbour of P.
How many people sit between R and V?
