Twelve buildings are arranged in two parallel rows of six each, facing each other. Row 1 consists of buildings A, B, C, D, E, and F facing east, while Row 2 has buildings J, K, L, M, N, and O facing west. 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 in F and L is 5.
- The number of buildings between D and F equals the number between J and L.
- K, with 12 offices, is second to the left of J.
- The difference between the offices in 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 fewer 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 in 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 fewer than J.

**Question:** Which building has the maximum number of offices?

Question

Twelve buildings are arranged in two parallel rows of six each, facing each other. Row 1 consists of buildings A, B, C, D, E, and F facing east, while Row 2 has buildings J, K, L, M, N, and O facing west. 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 in F and L is 5.
- The number of buildings between D and F equals the number between J and L.
- K, with 12 offices, is second to the left of J.
- The difference between the offices in 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 fewer 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 in 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 fewer than J.

**Question:** Which building has the maximum number of offices?

Accepted Answer

**Solution:**

1. From the clues, we know F is second from either end in Row 1, so F is either 2nd from left or right. Since there are 6 buildings, positions are 1 to 6.

2. F has 22 offices.

3. The difference between offices in F and L is 5, so L has either 17 or 27 offices. Since max is 28, L can have 17 or 27.

4. L has a prime number of offices. Among 17 and 27, 17 is prime, so L has 17 offices.

5. K has 12 offices and is second to the left of J.

6. J has a perfect square number of offices and more than D.

7. M has 15 offices less than J.

8. M has 15 offices (given indirectly as M is second to the right of building with 15 offices).

9. The difference between offices in K and L equals offices in B. K=12, L=17, difference=5, so B has 5 offices.

10. C has 16 offices and is third to the right of B.

11. O has two offices less than N, and N has fewer offices than L (17).

12. E has offices multiple of 11 and is to the right of building with 18 offices.

13. The difference between offices in O and A equals offices in M (15).

14. Using these clues and the relative positions, after arranging and calculating, J emerges as the building with the maximum number of offices.

**Answer:** J

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