Eleven seats are arranged in a single row numbered 1 to 11 from West to East. Three seats are vacant, and no two vacant seats are adjacent. All persons face North and have different ages. Given the following conditions:

- Three persons sit between A and B.
- The person aged 32 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 is as many years older than H as B is younger than D.
- C sits 3rd to the left of A.
- One person sits between G and F, who is 40 years old.
- The sum of ages of D and G is 82.
- H sits immediately to the left of a vacant seat.
- H's age is half the age of the person sitting at seat number 11.
- Persons aged 26 and 28 sit at odd-numbered seats.
- D sits to the left of the person aged 22 and to the right of the person aged 28.
- No vacant seat is between H and the person aged 22.

Which of the following statements about C is true?

Question

Eleven seats are arranged in a single row numbered 1 to 11 from West to East. Three seats are vacant, and no two vacant seats are adjacent. All persons face North and have different ages. Given the following conditions:

- Three persons sit between A and B.
- The person aged 32 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 is as many years older than H as B is younger than D.
- C sits 3rd to the left of A.
- One person sits between G and F, who is 40 years old.
- The sum of ages of D and G is 82.
- H sits immediately to the left of a vacant seat.
- H's age is half the age of the person sitting at seat number 11.
- Persons aged 26 and 28 sit at odd-numbered seats.
- D sits to the left of the person aged 22 and to the right of the person aged 28.
- No vacant seat is between H and the person aged 22.

Which of the following statements about C is true?

Accepted Answer

**Solution:**

1. Since A's seat number is less than 6 and C sits 3rd to the left of A, C must be seated at a position less than A's seat number minus 3. This makes it impossible for C to be at seat number 1 because if A were at seat 4 or 5, C would be at seat 1 or 2 respectively. But seat 1 is the extreme left, and with the vacant seats and other constraints, C cannot occupy seat 1.

2. The condition that three persons sit between A and B and the ages and neighbors of A, B, D, and E restrict the seating such that C's seat is fixed accordingly.

3. The age of C is not 22 years because the person aged 22 sits to the right of D, and D's position is constrained by the ages 26 and 28 sitting at odd seats.

4. Two persons sitting between A and C is incorrect because the problem states C sits 3rd to the left of A, which means there are exactly two seats between them, but the problem clarifies that the count of persons sitting between does not exclude vacant seats, so this option is misleading.

Hence, the only correct statement is that C does not sit at seat number 1.

**Answer:** C doesn’t sit at seat number 1

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