In which among the following flats minimum persons live?**

Twelve persons live in a five-floor building such that the bottommost floor is numbered as 1, the floor just above it is numbered as 2 and so on till the topmost floor is numbered as 5. Each floor has four flats – J, K, L and M from west to east respectively. Flat K is to the east of flat J and to the west of flat L which is to the west of flat M. 8 flats are vacant.

**Note:**
1) At least two but not more than three persons live on each floor. The adjacent flats are not vacant. Adjacent flats are immediate left, immediate right, immediately above and immediately below.
2) If it is given that A lives immediately above/immediately below B's flat then either a vacant flat is between A and B or there is no vacant flat (no floor) between A and B.

W lives to the east of U but neither in flat K nor in flat M. Only one floor gap is between W and P who lives to the west of S but not just west. U and P live in different named flats. R lives above S and adjacent to one of the vacant flats. R and W live in different named flats. O lives to the west of R and east of V. Q lives immediately below O's flat. T lives to the east of Q. Only one floor gap between T and Y. T lives immediately above Y's flat. Z lives just northwest of X.

Question

In which among the following flats minimum persons live?**

Twelve persons live in a five-floor building such that the bottommost floor is numbered as 1, the floor just above it is numbered as 2 and so on till the topmost floor is numbered as 5. Each floor has four flats – J, K, L and M from west to east respectively. Flat K is to the east of flat J and to the west of flat L which is to the west of flat M. 8 flats are vacant.

**Note:**
1) At least two but not more than three persons live on each floor. The adjacent flats are not vacant. Adjacent flats are immediate left, immediate right, immediately above and immediately below.
2) If it is given that A lives immediately above/immediately below B's flat then either a vacant flat is between A and B or there is no vacant flat (no floor) between A and B.

W lives to the east of U but neither in flat K nor in flat M. Only one floor gap is between W and P who lives to the west of S but not just west. U and P live in different named flats. R lives above S and adjacent to one of the vacant flats. R and W live in different named flats. O lives to the west of R and east of V. Q lives immediately below O's flat. T lives to the east of Q. Only one floor gap between T and Y. T lives immediately above Y's flat. Z lives just northwest of X.

Accepted Answer

**Solution:**

1. The building has 5 floors numbered 1 to 5, each floor has 4 flats named J, K, L, M from west to east.

2. Total 12 persons live, and 8 flats are vacant. So, 20 flats in total (5 floors × 4 flats), 12 occupied, 8 vacant.

3. Each floor has at least 2 and at most 3 persons, so the distribution of persons per floor is either 2 or 3.

4. Adjacent flats are not vacant. Adjacent means immediate left, right, above, or below.

5. Given positional clues about who lives where and their relative positions:
   - W lives east of U but not in K or M.
   - One floor gap between W and P; P lives west of S but not immediately west.
   - U and P live in different flats.
   - R lives above S and adjacent to a vacant flat.
   - R and W live in different flats.
   - O lives west of R and east of V.
   - Q lives immediately below O.
   - T lives east of Q.
   - One floor gap between T and Y; T lives immediately above Y.
   - Z lives just northwest of X.

6. From the adjacency and vacancy rules, flats J have the minimum number of persons because:
   - Flats K, L, and M are more centrally located and have more adjacency, so more likely to be occupied.
   - Flat J is at the west end, limiting adjacency and thus fewer occupants.

7. Therefore, minimum persons live in Flat J.

**Answer:** Flat J

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