Twelve buildings are arranged in two parallel rows with 6 buildings each. Row 1 (A, B, C, D, E, F) faces east, and Row 2 (J, K, L, M, N, O) faces west, with each building facing the corresponding building in the opposite row. Each building has a unique number of offices ranging between 5 and 28. Given the following clues:

- M is second to the right of the building with 15 offices.
- The number of buildings to the right of M is one less than the number of buildings to the left of L.
- L has a prime number of offices.
- The building facing M is second to the left of the building immediately right of D.
- F, which has 22 offices, is second from either end.
- The difference between the offices of F and L is 5.
- The number of buildings between D and F equals the number between J and L.
- K, having 12 offices, is second to the left of J.
- The difference between the offices of K and L equals the number of offices in B.
- C is third to the right of B, and B does not face M.
- C has 16 offices.
- O has two offices less than N.
- N has fewer offices than L.
- The number of offices in E is a multiple of 11.
- E is to the right of the building with 18 offices.
- The difference between the offices of O and A equals the number of offices in M.
- J has a perfect square number of offices and more than D.
- M has 15 offices less than J.

Which of the following building-office number combinations is correct?

Question

Twelve buildings are arranged in two parallel rows with 6 buildings each. Row 1 (A, B, C, D, E, F) faces east, and Row 2 (J, K, L, M, N, O) faces west, with each building facing the corresponding building in the opposite row. Each building has a unique number of offices ranging between 5 and 28. Given the following clues:

- M is second to the right of the building with 15 offices.
- The number of buildings to the right of M is one less than the number of buildings to the left of L.
- L has a prime number of offices.
- The building facing M is second to the left of the building immediately right of D.
- F, which has 22 offices, is second from either end.
- The difference between the offices of F and L is 5.
- The number of buildings between D and F equals the number between J and L.
- K, having 12 offices, is second to the left of J.
- The difference between the offices of K and L equals the number of offices in B.
- C is third to the right of B, and B does not face M.
- C has 16 offices.
- O has two offices less than N.
- N has fewer offices than L.
- The number of offices in E is a multiple of 11.
- E is to the right of the building with 18 offices.
- The difference between the offices of O and A equals the number of offices in M.
- J has a perfect square number of offices and more than D.
- M has 15 offices less than J.

Which of the following building-office number combinations is correct?

Accepted Answer

**Solution:**

1. **Identify positions and directions:**
   - Row 1 (A-F) faces east.
   - Row 2 (J-O) faces west.
   - Each building faces the corresponding building in the opposite row.

2. **Position of F:**
   - F is second from either end in Row 1, so F is either at position 2 or 5.
   - Since F has 22 offices, note this for later.

3. **Position of M and building with 15 offices:**
   - M is second to the right of the building with 15 offices.
   - Since M is in Row 2, and buildings face each other, this helps fix positions.

4. **Prime number of offices for L and difference with F:**
   - L has prime number offices.
   - Difference between offices of F (22) and L is 5, so L can be 17 or 27.
   - Since max offices are 28, L = 17.

5. **Offices of K and B:**
   - K has 12 offices and is second to the left of J.
   - The difference between offices of K (12) and L (17) is 5, which equals offices in B.
   - So, B has 5 offices.

6. **Offices of C:**
   - C has 16 offices and is third to the right of B.

7. **Offices of J and M:**
   - J has a perfect square number of offices and more than D.
   - M has 15 offices less than J.
   - Possible perfect squares under 28: 16, 25.
   - J cannot be 16 (C has 16), so J = 25.
   - Then M = 25 - 15 = 10 offices.

8. **Offices of O and N:**
   - O has two offices less than N.
   - N has fewer offices than L (17), so N < 17.
   - Possible N = 15, O = 13.

9. **Offices of E:**
   - Offices in E are multiple of 11.
   - Possible multiples under 28: 11, 22.
   - E is to the right of building with 18 offices.
   - So, 18 offices building is left of E.

10. **Offices of D:**
    - D has 18 offices (from above clue).

11. **Offices of A:**
    - Difference between offices of O (13) and A equals offices in M (10).
    - So, A = 3 or 23.
    - Since minimum offices are 5, A = 23.

12. **Offices of J and D:**
    - J (25) > D (18), consistent.

**Answer:** The correct combination is **D - 18** offices.

This matches option (c).

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