Ten people are sitting in two parallel rows containing 5 people each, in such a way that there is equal distance between adjacent persons. In Row 1 – A, B, C, D and E are seated and all of them are facing the south. In Row 2 – P, Q, R, S and T are seated and all of them are facing the north. Thus, each person is facing another person from the other row. B is sitting third to the right of A. P is facing an immediate neighbour of A. R is sitting third to the left of P. D is sitting second to the left of the person who is facing T. D is not sitting at any of the extreme ends of the row. C is facing Q. Who is facing E?
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Seating Arrangement Puzzle Solution
This problem involves a linear seating arrangement with two parallel rows of five people each, facing opposite directions. We need to determine the exact position of each person to answer the question about who is facing E.
- Row 1: A, B, C, D, E are seated and face South.
- Row 2: P, Q, R, S, T are seated and face North.
- Each person in Row 1 faces exactly one person in Row 2.
Let's denote the seats in each row from left to right as Seat 1, Seat 2, Seat 3, Seat 4, and Seat 5.
For Row 1 (facing South): Right is towards Seat 1, Left is towards Seat 5.
For Row 2 (facing North): Right is towards Seat 5, Left is towards Seat 1.
Analyzing the Clues
- B is sitting third to the right of A (Row 1, South).
For someone facing South, their right is towards the smaller seat number. If A is at Seat $x$, B is at Seat $x-3$. This is only possible if A is at Seat 4 (B at Seat 1) or A is at Seat 5 (B at Seat 2).
Possible R1 arrangements: (B, \_, \_, A, \_) or (\_, B, \_, \_, A) - P is facing an immediate neighbour of A.
The person facing P is in Row 1, and they are next to A in Row 1. If P is at Seat $y$ in R2, the person they face is at Seat $y$ in R1. This person at R1-Seat $y$ must be adjacent to A in R1. - R is sitting third to the left of P (Row 2, North).
For someone facing North, their left is towards the smaller seat number. If P is at Seat $y$, R is at Seat $y-3$. This is only possible if P is at Seat 4 (R at Seat 1) or P is at Seat 5 (R at Seat 2).
Possible R2 arrangements: (R, \_, \_, P, \_) or (\_, R, \_, \_, P) - D is sitting second to the left of the person who is facing T (Row 1, South).
Let the person facing T in Row 1 be Y, sitting at Seat $y$. T is in R2, so T must be at Seat $y$ in R2. D is in R1 at Seat $d$. D is 2nd left of Y (in R1, South). Left for South-facing is towards larger seat numbers. If Y is at Seat $y$, 1st left is $y+1$, 2nd left is $y+2$. So, $d = y+2$. - D is not sitting at any of the extreme ends of the row (Row 1).
D is not at Seat 1 or Seat 5 in Row 1. D must be at Seat 2, 3, or 4. - C is facing Q.
C is in R1, Q is in R2. They must be at the same seat number. If C is at R1-Seat $z$, Q is at R2-Seat $z$.
Step-by-Step Deduction
Let's combine the clues to build the arrangement.
From Clue 1 and 3, we have two main scenarios for A/B and P/R positions:
Scenario 1: A at R1-4, B at R1-1 (from Clue 1) AND P at R2-5, R at R2-2 (from Clue 3).
- R1: (B, \_, \_, A, \_)
- R2: (\_, R, \_, \_, P)
- Check Clue 2: P (R2-5) faces the person at R1-5. This person must be an immediate neighbour of A (R1-4). The person at R1-5 is indeed a neighbour of A at R1-4. Let's call the person at R1-5 as X. R1: (B, \_, \_, A, X).
- In R1, B is at 1, A at 4, X at 5. Remaining people for seats 2, 3 are C, D. Remaining person for Seat 5 (X) is E. So, X=E. R1: (B, \_, \_, A, E). Remaining for 2, 3 are C, D.
- Clue 5: D is not at ends (1 or 5). B is at 1, E is at 5. So D must be at seat 2 or 3.
- Clue 6: C faces Q (same seat number). Possible seats for C/Q are 2 or 3 (seats 1, 4, 5 are taken by B, A, E in R1 and \_, R, P in R2). If C is at R1-2, Q is at R2-2, but R is at R2-2. So C must be at R1-3, and Q at R2-3.
- This gives R1: (B, D, C, A, E) because D must be at seat 2 if C is at seat 3 and E is at seat 5.
- And R2: (\_, R, Q, \_, P). Remaining in R2 for seats 1, 4 are S, T. R2: (S/T, R, Q, S/T, P).
- Let's check Clue 4: D (R1-2) is 2nd left of person facing T (R1-y). Left in R1 (South) is towards seat 5. $d = y+2$. D is at 2, so $2 = y+2 \implies y=0$. This is not a valid seat number. Scenario 1 leads to a contradiction with Clue 4 if "left" means the person's left.
Scenario 2: A at R1-5, B at R1-2 (from Clue 1) AND P at R2-4, R at R2-1 (from Clue 3).
- R1: (\_, B, \_, \_, A)
- R2: (R, \_, \_, P, \_)
- Check Clue 2: P (R2-4) faces the person at R1-4. This person must be an immediate neighbour of A (R1-5). The person at R1-4 is indeed a neighbour of A at R1-5. Let's call the person at R1-4 as X. R1: (\_, B, \_, X, A).
- In R1, B is at 2, A at 5, X at 4. Remaining people for seats 1, 3 are C, D, E. Remaining person for Seat 4 (X) is C, D or E.
- Clue 5: D is not at ends (1 or 5). D cannot be at 5 (A is there). D could be at 1, 3, or 4. But D cannot be at 1. So D is at 3 or 4.
- Clue 6: C faces Q (same seat number). Possible seats for C/Q: 1, 3, 4. (Seats 2, 5 are taken by B, A in R1 and R, P in R2).
- If C is at R1-1, Q is at R2-1, but R is at R2-1. Not possible.
- If C is at R1-3, Q is at R2-3. Possible.
- If C is at R1-4, Q is at R2-4, but P is at R2-4. Not possible.
- So, C is at R1-3, Q is at R2-3. R1: (\_, B, C, X, A). X is D or E. D is at 3 or 4. C is at 3. So D must be at 4. X=D. E must be at seat 1. R1: (E, B, C, D, A)
- R2: (R, \_, Q, P, \_). Remaining in R2 for seats 2, 5 are S, T. R2: (R, S/T, Q, P, S/T).
Let's check Clue 4 with this arrangement: D (R1-4) is 2nd left of person facing T (R1-y). Left in R1 (South) is towards seat 5. $d = y+2$. D is at 4, so $4 = y+2 \implies y=2$. So, the person facing T is at R1-Seat 2. Who is at R1-Seat 2? B. Thus, B faces T. B is at R1-2, T must be at R2-2.
In our current R2 arrangement (R, S/T, Q, P, S/T), Seat 2 has S/T. If T is at R2-2, then S must be at R2-5.
Final Arrangement:
| Row 1 (South) | Seat 1 | Seat 2 | Seat 3 | Seat 4 | Seat 5 |
| Person | E | B | C | D | A |
| Row 2 (North) | Seat 1 | Seat 2 | Seat 3 | Seat 4 | Seat 5 |
| Person | R | T | Q | P | S |
Let's verify this final arrangement against all clues:
- Clue 1: B (R1-2) is 3rd right of A (R1-5). Facing South, right is towards Seat 1. Seat 5 → 4 (1st right) → 3 (2nd right) → 2 (3rd right). B is at Seat 2. Correct.
- Clue 2: P (R2-4) faces D (R1-4). A is at R1-5. D is an immediate neighbour of A. Correct.
- Clue 3: R (R2-1) is 3rd left of P (R2-4). Facing North, left is towards Seat 1. Seat 4 → 3 (1st left) → 2 (2nd left) → 1 (3rd left). R is at Seat 1. Correct.
- Clue 4: D (R1-4) is 2nd left of the person facing T (B at R1-2). Facing South, left is towards Seat 5. Seat 2 → 3 (1st left) → 4 (2nd left). D is at Seat 4. Correct.
- Clue 5: D is not at ends. D is at R1-4. Correct.
- Clue 6: C (R1-3) faces Q (R2-3). Correct.
All clues are satisfied by this arrangement.
Answering the Question
The question asks: Who is facing E?
E is in Row 1 at Seat 1. The person facing E is in Row 2 at the same seat number, Seat 1.
Looking at Row 2: R T Q P S.
The person at Seat 1 in Row 2 is R.
Therefore, R is facing E.
Revision Table: Seating Puzzle Details
| Row | Direction | Seat 1 | Seat 2 | Seat 3 | Seat 4 | Seat 5 |
| Row 1 | South | E | B | C | D | A |
| Row 2 | North | R | T | Q | P | S |
Additional Information: Linear Seating Puzzles
Linear seating arrangement puzzles are common in reasoning sections of competitive exams. They typically involve people sitting in one or more rows, facing a specific direction (North, South, East, West, or sometimes towards/away from the center in a circular arrangement).
Key aspects to remember:
- Understand the facing direction: This dictates which side is "left" and which is "right" for each person. Draw diagrams clearly marking the direction.
- Relative positions: Clues often involve terms like "to the left of", "to the right of", "second to the left", "immediate neighbour", etc. Be careful with directions, especially when people are facing opposite ways.
- Absolute positions: Clues might mention ends of the row or specific numbered positions.
- Facing: When people face each other in parallel rows, they are at the same relative position (e.g., the person at Seat 1 in Row 1 faces the person at Seat 1 in Row 2).
- Negative information: Clues like "X is not at an end" or "Y is not a neighbour of Z" are crucial for eliminating possibilities.
Solving these puzzles usually involves drawing diagrams and iterating through possibilities based on the clues, eliminating contradictions as you go. Start with the most restrictive clues or those that connect multiple people.
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Ten people are sitting in two parallel rows containing 5 people each, in such a way that there is equal distance between adjacent persons.
In Row 1 – A, B, C, D and E are seated and all of them are facing the north.
In Row 2 – P, Q, R, S and T are seated and all of them are facing the south.
Thus, each person is facing another person from the other row.
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Who is facing T?
Seven friends, A, B, C, D, E, F and G are sitting in a straight line facing the same direction. E is sitting at one extreme end. E is sitting second to the left of C. B is sitting between C and A, whereas G and A are not sitting at any extreme end. F is seated immediately right of D. Who is seated in the middle?
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Who sits at the extreme left end of the row?
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Who among the following is sitting in front of M?
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?
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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?
