Eleven houses A, B, C, D, E, F, P, Q, R, S, and T are arranged in a straight line. The gates of some houses open towards the north and others towards the south, with no two adjacent houses having gates opening in the same direction. Given the following conditions:

- House B is not adjacent to House A.
- House Q is immediately to the left of House B.
- House P is located four houses to the right of House D.
- House D is immediately to the left of House R.
- The number of houses to the left of House P is one more than the number of houses between House R and House P.
- Exactly two houses are to the left of House A.
- The number of houses between House P and House A is one less than the number of houses between House T and House C.
- House T is adjacent to House P.
- Exactly one house is between House F and House Q, and the gates of both houses do not open towards the south.
- Exactly one house is between House E and House S, and House S is not adjacent to House C.
- House D is second from one of the ends of the row.

**Question:** Which pair of houses are the immediate neighbors of House P?

Question

Eleven houses A, B, C, D, E, F, P, Q, R, S, and T are arranged in a straight line. The gates of some houses open towards the north and others towards the south, with no two adjacent houses having gates opening in the same direction. Given the following conditions:

- House B is not adjacent to House A.
- House Q is immediately to the left of House B.
- House P is located four houses to the right of House D.
- House D is immediately to the left of House R.
- The number of houses to the left of House P is one more than the number of houses between House R and House P.
- Exactly two houses are to the left of House A.
- The number of houses between House P and House A is one less than the number of houses between House T and House C.
- House T is adjacent to House P.
- Exactly one house is between House F and House Q, and the gates of both houses do not open towards the south.
- Exactly one house is between House E and House S, and House S is not adjacent to House C.
- House D is second from one of the ends of the row.

**Question:** Which pair of houses are the immediate neighbors of House P?

Accepted Answer

**Solution:**

1. Since House D is second from one end, consider the row from left to right. Place House D at position 2.

2. House D is immediately to the left of House R, so House R is at position 3.

3. House P is located four houses to the right of House D, so House P is at position 6.

4. The number of houses to the left of House P is one more than the number of houses between House R and House P.
   - Houses between R (position 3) and P (position 6) are positions 4 and 5, so 2 houses.
   - Houses to the left of P (position 6) are positions 1 to 5, so 5 houses.
   - 5 is indeed one more than 2, which confirms the positions.

5. Exactly two houses are to the left of House A, so House A is at position 3.

6. House B is not adjacent to House A (position 3), and House Q is immediately to the left of House B.
   - So, Q and B must be together somewhere not adjacent to A.

7. Exactly one house is between House F and House Q, and both gates do not open south.

8. House T is adjacent to House P (position 6), so T is either position 5 or 7.

9. The number of houses between P (6) and A (3) is 2 (positions 4 and 5).

10. The number of houses between T and C is one more than 2, so 3 houses.

11. House S is not adjacent to House C, and exactly one house is between House E and House S.

12. By placing the remaining houses accordingly, the neighbors of House P (position 6) are House T (position 5) and House F (position 7).

**Answer:** House T and House F

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