Seven friends – P, Q, R, S, T, U and V – sit in seven seats numbered 1 to 7 from left to right in a single row, all facing north. Each seat is occupied by exactly one person. The following information is known:
1. P sits between R and V, adjacent to both of them.
2. Q sits somewhere to the right of V, but Q and S are not adjacent to each other.
3. T sits at one of the two ends of the row.
4. Exactly two people sit between R and Q.
5. U does not sit at either end of the row.
6. S sits somewhere to the right of P.
7. R does not sit at either end of the row, and V sits somewhere to the right of R.
1. P sits between R and V, adjacent to both of them.
2. Q sits somewhere to the right of V, but Q and S are not adjacent to each other.
3. T sits at one of the two ends of the row.
4. Exactly two people sit between R and Q.
5. U does not sit at either end of the row.
6. S sits somewhere to the right of P.
7. R does not sit at either end of the row, and V sits somewhere to the right of R.
Question 1
Single correct option
Who sits in seat 4?
- A. P
- B. V
- C. Q
- D. U
Show answer and solution
Answer: (B) V
Deduction: Clues 1 and 7 give the block R–P–V (in that order, left to right). Clue 4 puts Q three seats to the right of R, i.e. immediately to the right of V: R P V Q. R is not at an end, so R is in seat 2 or 3 (the block R P V Q needs four seats, so R ≤ 4).
- If R = 3: R P V Q occupy 3–6; T must be at an end, U cannot be; remaining seats 1, 2, 7 for S, T, U → U = 2, and S must be right of P → S = 7, T = 1. But then Q (6) and S (7) are adjacent ✗.
- If R = 2: R P V Q occupy 2–5; remaining seats 1, 6, 7. U is not at an end → U = 6. S is not adjacent to Q (5) → S ≠ 6, and S right of P → S = 7, T = 1 ✓.
- R = 4 would need seats 4–7 for the block, leaving S (right of P) no seat ✗.
Final arrangement:
| Seat | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|
| Person | T | R | P | V | Q | U | S |
Seat 4 is occupied by V.
- If R = 3: R P V Q occupy 3–6; T must be at an end, U cannot be; remaining seats 1, 2, 7 for S, T, U → U = 2, and S must be right of P → S = 7, T = 1. But then Q (6) and S (7) are adjacent ✗.
- If R = 2: R P V Q occupy 2–5; remaining seats 1, 6, 7. U is not at an end → U = 6. S is not adjacent to Q (5) → S ≠ 6, and S right of P → S = 7, T = 1 ✓.
- R = 4 would need seats 4–7 for the block, leaving S (right of P) no seat ✗.
Final arrangement:
| Seat | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|
| Person | T | R | P | V | Q | U | S |
Seat 4 is occupied by V.
Question 2
Numerical answer
How many people sit between T and U?
Show answer and solution
Answer: 4
Deduction: Clues 1 and 7 give the block R–P–V (in that order, left to right). Clue 4 puts Q three seats to the right of R, i.e. immediately to the right of V: R P V Q. R is not at an end, so R is in seat 2 or 3 (the block R P V Q needs four seats, so R ≤ 4).
- If R = 3: R P V Q occupy 3–6; T must be at an end, U cannot be; remaining seats 1, 2, 7 for S, T, U → U = 2, and S must be right of P → S = 7, T = 1. But then Q (6) and S (7) are adjacent ✗.
- If R = 2: R P V Q occupy 2–5; remaining seats 1, 6, 7. U is not at an end → U = 6. S is not adjacent to Q (5) → S ≠ 6, and S right of P → S = 7, T = 1 ✓.
- R = 4 would need seats 4–7 for the block, leaving S (right of P) no seat ✗.
Final arrangement:
| Seat | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|
| Person | T | R | P | V | Q | U | S |
T is in seat 1 and U in seat 6; seats 2–5 (R, P, V, Q) lie between them: 4 people.
- If R = 3: R P V Q occupy 3–6; T must be at an end, U cannot be; remaining seats 1, 2, 7 for S, T, U → U = 2, and S must be right of P → S = 7, T = 1. But then Q (6) and S (7) are adjacent ✗.
- If R = 2: R P V Q occupy 2–5; remaining seats 1, 6, 7. U is not at an end → U = 6. S is not adjacent to Q (5) → S ≠ 6, and S right of P → S = 7, T = 1 ✓.
- R = 4 would need seats 4–7 for the block, leaving S (right of P) no seat ✗.
Final arrangement:
| Seat | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|
| Person | T | R | P | V | Q | U | S |
T is in seat 1 and U in seat 6; seats 2–5 (R, P, V, Q) lie between them: 4 people.
Question 3
Single correct option
Which of the following statements is true?
- A. S sits immediately to the right of Q
- B. R sits second from the left end
- C. P sits third from the right end
- D. U sits immediately to the left of Q
Show answer and solution
Answer: (B) R sits second from the left end
Deduction: Clues 1 and 7 give the block R–P–V (in that order, left to right). Clue 4 puts Q three seats to the right of R, i.e. immediately to the right of V: R P V Q. R is not at an end, so R is in seat 2 or 3 (the block R P V Q needs four seats, so R ≤ 4).
- If R = 3: R P V Q occupy 3–6; T must be at an end, U cannot be; remaining seats 1, 2, 7 for S, T, U → U = 2, and S must be right of P → S = 7, T = 1. But then Q (6) and S (7) are adjacent ✗.
- If R = 2: R P V Q occupy 2–5; remaining seats 1, 6, 7. U is not at an end → U = 6. S is not adjacent to Q (5) → S ≠ 6, and S right of P → S = 7, T = 1 ✓.
- R = 4 would need seats 4–7 for the block, leaving S (right of P) no seat ✗.
Final arrangement:
| Seat | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|
| Person | T | R | P | V | Q | U | S |
Check each: S (7) is not adjacent to Q (5) ✗; R is in seat 2, i.e. second from the left ✓; P (seat 3) is fifth from the right ✗; U (6) is to the right of Q (5), not the left ✗. Answer: R sits second from the left end.
- If R = 3: R P V Q occupy 3–6; T must be at an end, U cannot be; remaining seats 1, 2, 7 for S, T, U → U = 2, and S must be right of P → S = 7, T = 1. But then Q (6) and S (7) are adjacent ✗.
- If R = 2: R P V Q occupy 2–5; remaining seats 1, 6, 7. U is not at an end → U = 6. S is not adjacent to Q (5) → S ≠ 6, and S right of P → S = 7, T = 1 ✓.
- R = 4 would need seats 4–7 for the block, leaving S (right of P) no seat ✗.
Final arrangement:
| Seat | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|
| Person | T | R | P | V | Q | U | S |
Check each: S (7) is not adjacent to Q (5) ✗; R is in seat 2, i.e. second from the left ✓; P (seat 3) is fifth from the right ✗; U (6) is to the right of Q (5), not the left ✗. Answer: R sits second from the left end.
Question 4
Single correct option
If T and S interchange their seats, who will be third from the right end?
- A. U
- B. V
- C. Q
- D. P
Show answer and solution
Answer: (C) Q
Deduction: Clues 1 and 7 give the block R–P–V (in that order, left to right). Clue 4 puts Q three seats to the right of R, i.e. immediately to the right of V: R P V Q. R is not at an end, so R is in seat 2 or 3 (the block R P V Q needs four seats, so R ≤ 4).
- If R = 3: R P V Q occupy 3–6; T must be at an end, U cannot be; remaining seats 1, 2, 7 for S, T, U → U = 2, and S must be right of P → S = 7, T = 1. But then Q (6) and S (7) are adjacent ✗.
- If R = 2: R P V Q occupy 2–5; remaining seats 1, 6, 7. U is not at an end → U = 6. S is not adjacent to Q (5) → S ≠ 6, and S right of P → S = 7, T = 1 ✓.
- R = 4 would need seats 4–7 for the block, leaving S (right of P) no seat ✗.
Final arrangement:
| Seat | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|
| Person | T | R | P | V | Q | U | S |
After the swap: S R P V Q U T (seats 1–7). Third from the right is seat 5: Q. (The swap does not affect seats 2–6.)
- If R = 3: R P V Q occupy 3–6; T must be at an end, U cannot be; remaining seats 1, 2, 7 for S, T, U → U = 2, and S must be right of P → S = 7, T = 1. But then Q (6) and S (7) are adjacent ✗.
- If R = 2: R P V Q occupy 2–5; remaining seats 1, 6, 7. U is not at an end → U = 6. S is not adjacent to Q (5) → S ≠ 6, and S right of P → S = 7, T = 1 ✓.
- R = 4 would need seats 4–7 for the block, leaving S (right of P) no seat ✗.
Final arrangement:
| Seat | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|
| Person | T | R | P | V | Q | U | S |
After the swap: S R P V Q U T (seats 1–7). Third from the right is seat 5: Q. (The swap does not affect seats 2–6.)
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