Eleven seats are arranged in a single row facing North, numbered from 1 to 11 from West to East. Among these, three seats are vacant, and no two vacant seats are adjacent. Each seat is occupied by a person of a different age. The following conditions apply:

- Three persons sit between A and B.
- The person who is 32 years old sits immediately to the left of B.
- D and E are immediate neighbors of A, and A's seat number is less than 6.
- B's age is equally distant from H's and D's ages (B is as many years older than H as younger than D).
- C sits third to the left of A.
- One person sits between G and F, who is 40 years old.
- The sum of the ages of D and G is 82.
- H sits immediately to the left of one of the vacant seats.
- H's age is half the age of the person sitting in seat number 11.
- Persons aged 26 and 28 years sit in odd-numbered seats.
- D sits to the left of the person aged 22 years and to the right of the person aged 28 years.
- No vacant seat is between H and the person aged 22 years.

**Question:** In which seat is the person aged 26 years sitting?

Question

Eleven seats are arranged in a single row facing North, numbered from 1 to 11 from West to East. Among these, three seats are vacant, and no two vacant seats are adjacent. Each seat is occupied by a person of a different age. The following conditions apply:

- Three persons sit between A and B.
- The person who is 32 years old sits immediately to the left of B.
- D and E are immediate neighbors of A, and A's seat number is less than 6.
- B's age is equally distant from H's and D's ages (B is as many years older than H as younger than D).
- C sits third to the left of A.
- One person sits between G and F, who is 40 years old.
- The sum of the ages of D and G is 82.
- H sits immediately to the left of one of the vacant seats.
- H's age is half the age of the person sitting in seat number 11.
- Persons aged 26 and 28 years sit in odd-numbered seats.
- D sits to the left of the person aged 22 years and to the right of the person aged 28 years.
- No vacant seat is between H and the person aged 22 years.

**Question:** In which seat is the person aged 26 years sitting?

Accepted Answer

**Solution:**

1. There are 11 seats in a row facing North, numbered 1 to 11 from West to East, with 3 vacant seats such that no two vacant seats are adjacent.

2. A's seat number is less than 6, and D and E are immediate neighbors of A.

3. C sits third to the left of A, so if A is at seat *x*, C is at seat *x-3*.

4. Three persons sit between A and B, so the difference between their seat numbers is 4.

5. The person aged 32 sits immediately to the left of B.

6. B's age is equally distant from H's and D's ages, meaning:  B - H = D - B.

7. One person sits between G and F, with F aged 40.

8. The sum of ages of D and G is 82.

9. H sits immediately to the left of a vacant seat.

10. H's age is half the age of the person sitting at seat 11.

11. Persons aged 26 and 28 sit in odd-numbered seats.

12. D sits left of the person aged 22 and right of the person aged 28.

13. No vacant seat is between H and the person aged 22.

**Stepwise deduction:**

- Since A's seat number is less than 6, possible seats for A are 2, 3, 4, or 5 (1 is unlikely because C would be at seat -2, which is invalid).

- If A is at seat 5, then C is at seat 2 (5 - 3 = 2).

- D and E are neighbors of A, so D and E occupy seats 4 and 6 (or 6 and 4), but since A is at 5, neighbors are seats 4 and 6.

- B is 4 seats away from A, so if A is at 5, B can be at seat 1 or 9.

- The person aged 32 sits immediately to the left of B, so if B is at seat 9, 32-year-old is at seat 8.

- H sits immediately to the left of a vacant seat and no vacant seat is between H and the person aged 22.

- Persons aged 26 and 28 sit at odd seats.

- D sits between persons aged 28 (left) and 22 (right).

- Using these clues and the sum of ages of D and G is 82, and F is 40 years old.

- After placing all persons according to the conditions, the person aged 26 is found to be sitting at seat number 5.

**Answer:** Seat number 5

Answer

Answer

Answer

Answer