Ten people—J, K, L, M, N, O, P, Q, R, and S —live in a building with five floors and two flats (Flat 1 and Flat 2) on each floor. The floors are numbered from 1 to 5 (1 being the lowermost floor and 5 being the topmost floor).

Note I: Each floor has two flats viz., Flat-1 and Flat-2, where Flat 1 is to the west of Flat 2.

Note II: Flat 1 of floor 2 is immediately above Flat 1 of floor 1 and immediately below Flat 1 of floor 3 and so on. Similarly Flat 2 of floor 2 is immediately above Flat 2 of floor 1 and immediately below Flat 2 of floor 3 and so on.

Note III: The area of each flat is equal.

Note IV: Only two persons live on each floor and only one person lives in each flat.

L lives on an even -numbered floor in Flat -1. P lives in Flat -2 of the topmost floor. N lives west of Q. N lives on a floor immediately below the L’s floor. K and R live on the same named flat. K and L lives in a different named flat. Only one floor is between K and O. K lives below O. S lives to the west of P. M lives immediately below O, but not in the same named flat. One floor between J’s floor and L’s floor.

Who lives in Flat 2 on the third floor?

To determine who lives in Flat 2 on the third floor, let us analyze the clues step-by-step and reconstruct the arrangement of the ten people (J, K, L, M, N, O, P, Q, R, and S) living in the 5 floors (numbered 1 to 5 from bottom to top) and 2 flats (Flat 1 is to the west of Flat 2).

Let us represent each position as (Floor, Flat). There are ten positions:
Floor 5: (5, Flat 1), (5, Flat 2)
Floor 4: (4, Flat 1), (4, Flat 2)
Floor 3: (3, Flat 1), (3, Flat 2)
Floor 2: (2, Flat 1), (2, Flat 2)
Floor 1: (1, Flat 1), (1, Flat 2)

Step 1: Place P and S using the topmost floor clues.
Clue: "P lives in Flat -2 of the topmost floor."
⇒ P is at (5, Flat 2).
Clue: "S lives to the west of P."
⇒ Since Flat 1 is to the west of Flat 2, S must be at (5, Flat 1).

Step 2: Place L and N.
Clue: "L lives on an even-numbered floor in Flat -1."
Since Floor 4 and Floor 2 are the even-numbered floors:
Case A: L is at (4, Flat 1).
Case B: L is at (2, Flat 1).
Clue: "N lives west of Q."
⇒ N is in Flat 1 and Q is in Flat 2 on the same floor.
Clue: "N lives on a floor immediately below the L’s floor."
If Case A is true (L at Floor 4), then N lives on Floor 3. Since N is west of Q, N is at (3, Flat 1) and Q is at (3, Flat 2).
If Case B is true (L at Floor 2), then N lives on Floor 1. N is at (1, Flat 1) and Q is at (1, Flat 2).

Step 3: Analyze O, K, and M.
Clue: "K and L lives in a different named flat."
Since L is in Flat 1, K must be in Flat 2.
Clue: "K lives below O." and "Only one floor is between K and O."
This means O is two floors above K. Since K is in Flat 2, K and O are on floors separated by one floor.
Clue: "M lives immediately below O, but not in the same named flat."
Since M is immediately below O, M is on the floor just below O's floor. Since they are not in the same named flat, and they cannot overlap, we can analyze the positions.
Clue: "One floor between J’s floor and L’s floor."

Let us test Case A: L is at (4, Flat 1).
Then N is at (3, Flat 1) and Q is at (3, Flat 2).
J's floor must be 2 (since L is on Floor 4, and one floor is between J and L).
This leaves Floor 1 and Floor 2 available for other placements. Since K must be below O with one floor between them, O could be on Floor 3 or 4 or 5, and K on Floor 1 or 2 or 3 respectively.
If O is on Floor 3 (Flat 1 or 2) and K is on Floor 1 (Flat 2):
Since N is at (3, Flat 1) and Q is at (3, Flat 2), Floor 3 is completely occupied. Thus O cannot be on Floor 3. This is a contradiction.
If O is on Floor 4: Since L is at (4, Flat 1), O must be at (4, Flat 2). K would be on Floor 2, Flat 2 (since K is in Flat 2).
If O is at (4, Flat 2), M lives immediately below O but not in the same named flat. The floor immediately below O (Floor 4) is Floor 3. Since O is in Flat 2, M must be in Flat 1. So M is at (3, Flat 1). But Floor 3 has N at (3, Flat 1), which is a conflict. Thus, Case A is invalid.

Now let us test Case B: L is at (2, Flat 1).
Then N is at (1, Flat 1) and Q is at (1, Flat 2).
Since one floor is between J and L, J's floor must be Floor 4 (L is on Floor 2).
Since K is in Flat 2, and there is one floor between K and O (with K below O), the possible floors for K and O are:
- K at Floor 2, O at Floor 4.
- K at Floor 3, O at Floor 5.
Since Floor 5 has S at (5, Flat 1) and P at (5, Flat 2), O cannot be on Floor 5. Thus, O must be on Floor 4 and K must be on Floor 2.
Since K is in Flat 2, K is at (2, Flat 2).
Since L is at (2, Flat 1) and K is at (2, Flat 2), Floor 2 is fully occupied.
O is on Floor 4. Since J is also on Floor 4, and K is in Flat 2, let's determine the flats. K is at (2, Flat 2). O can be at (4, Flat 1) or (4, Flat 2).
Clue: "M lives immediately below O, but not in the same named flat."
The floor immediately below O (Floor 4) is Floor 3. M is on Floor 3.
If O is at (4, Flat 1), M must be in Flat 2, so M is at (3, Flat 2). Consequently, J is at (4, Flat 2).
If O is at (4, Flat 2), M must be in Flat 1, so M is at (3, Flat 1). Consequently, J is at (4, Flat 1).
Let us check the remaining clue: "K and R live on the same named flat."
Since K is in Flat 2, R must also be in Flat 2.
Looking at the occupied positions in Flat 2:
Floor 5: P (Flat 2)
Floor 4: Either J or O (one of them is in Flat 2)
Floor 3: Must contain R in Flat 2, since Floor 1 has Q (Flat 2) and Floor 2 has K (Flat 2).
Therefore, R must live in Flat 2 on Floor 3.
If R is at (3, Flat 2), then M must be at (3, Flat 1), which means O is at (4, Flat 2) and J is at (4, Flat 1).

Let's double-check the final arrangement:
Floor 5: S (Flat 1), P (Flat 2)
Floor 4: J (Flat 1), O (Flat 2)
Floor 3: M (Flat 1), R (Flat 2)
Floor 2: L (Flat 1), K (Flat 2)
Floor 1: N (Flat 1), Q (Flat 2)

All conditions are satisfied:
- L is on Floor 2 (even) in Flat 1.
- P is in Flat 2 of Floor 5.
- N (1, Flat 1) lives west of Q (1, Flat 2).
- N lives immediately below L.
- K (2, Flat 2) and R (3, Flat 2) live in Flat 2.
- K (Flat 2) and L (Flat 1) live in different flats.
- Only one floor is between K (Floor 2) and O (Floor 4), and K lives below O.
- S (5, Flat 1) is west of P (5, Flat 2).
- M (3, Flat 1) lives immediately below O (4, Flat 2), and they are in different flats (Flat 1 vs Flat 2).
- One floor is between J (Floor 4) and L (Floor 2).

Thus, the person who lives in Flat 2 on the third floor is R.