Sixteen individuals — A, B, C, E, N, O, P, Q, R, S, T, U, V, W, X, and Y — reside in two flats (Flat 1 and Flat 2) of a four-floor building. The floors are numbered 1 to 4 from bottom to top. Flat 1 is located to the west of Flat 2. Flat 1 on floor 2 is directly above Flat 1 on floor 1, and similarly for Flat 2. There are eight married couples, each couple living together on the same floor and in the same flat. Names starting with a vowel indicate females, who live only on even-numbered floors. The information below is given:

- A lives just above the flat of P’s spouse.
- A’s spouse lives in an odd-numbered flat.
- O and Q live on the same floor.
- T lives to the northeast of U and below E.
- Q and E do not live in the same flat.
- B lives on an even-numbered floor and two floors above N.
- S lives to the southwest of B but not below N.
- R lives to the north of X and is not married to A.
- The spouse of X lives to the east of Y.
- C is not the spouse of Y or X.
- V and U live in the same flat and share the same gender.
- W and Q have the same gender.

Based on the above, on which flat and floor does S live?

Question

Sixteen individuals — A, B, C, E, N, O, P, Q, R, S, T, U, V, W, X, and Y — reside in two flats (Flat 1 and Flat 2) of a four-floor building. The floors are numbered 1 to 4 from bottom to top. Flat 1 is located to the west of Flat 2. Flat 1 on floor 2 is directly above Flat 1 on floor 1, and similarly for Flat 2. There are eight married couples, each couple living together on the same floor and in the same flat. Names starting with a vowel indicate females, who live only on even-numbered floors. The information below is given:

- A lives just above the flat of P’s spouse.
- A’s spouse lives in an odd-numbered flat.
- O and Q live on the same floor.
- T lives to the northeast of U and below E.
- Q and E do not live in the same flat.
- B lives on an even-numbered floor and two floors above N.
- S lives to the southwest of B but not below N.
- R lives to the north of X and is not married to A.
- The spouse of X lives to the east of Y.
- C is not the spouse of Y or X.
- V and U live in the same flat and share the same gender.
- W and Q have the same gender.

Based on the above, on which flat and floor does S live?

Accepted Answer

**Solution:**

1. Since names starting with vowels are females and they live on even floors, females are A, E, O, U.

2. B lives on an even floor and two floors above N, so if N is on floor 1, B is on floor 3.

3. S lives southwest of B but not below N, so S must be on floor 3 or above and to the southwest of B.

4. A lives just above P’s spouse’s flat. Since A’s spouse lives in an odd-numbered flat, A is on an odd flat above P’s spouse.

5. O and Q live on the same floor, but Q and E are in different flats.

6. T lives northeast of U and below E, so E is on a higher floor than T and U.

7. R lives north of X and is not married to A.

8. The spouse of X lives east of Y, and C is not spouse of Y or X.

9. V and U live in the same flat and have the same gender.

10. W and Q share the same gender.

By logically placing these individuals according to the directions and floor constraints, S is found to be living in Flat 1 on floor 3.

**Answer:** Flat 1, floor 3

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