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.

How many persons live between S and N in the same numbered flat?

The correct answer is Three.

Let us construct the step-by-step placement of the ten people (J, K, L, M, N, O, P, Q, R, and S) in the building. The building has 5 floors (numbered 1 to 5 from bottom to top) and two flats on each floor (Flat 1 is to the west of Flat 2).

Step 1: Placement of P and S
According to the clues:

• P lives in Flat 2 of the topmost floor (Floor 5). Thus, P is at Floor 5, Flat 2.
• S lives to the west of P. Since Flat 1 is to the west of Flat 2, S must be at Floor 5, Flat 1.

Step 2: Placement of L, N, and Q
We are given:

• L lives on an even-numbered floor in Flat 1. The even floors are Floor 2 and Floor 4. Let's analyze the two possibilities:
• N lives on the floor immediately below L.
• N lives to the west of Q, which means N is in Flat 1 and Q is in Flat 2 on the same floor.

Let us test the case where L is on Floor 4:
If L is at Floor 4, Flat 1, then N and Q must be on Floor 3 (immediately below L), with N at Floor 3, Flat 1 and Q at Floor 3, Flat 2.
One floor is between J's floor and L's floor. Since L is on Floor 4, J must be on Floor 2.
Now we consider K and O:
Only one floor is between K and O, and K lives below O. K and L live in different named flats, so K must live in Flat 2 (since L is in Flat 1).
If K is in Flat 2, the possible positions for K to have one floor between it and O are Floor 1 or Floor 2 (O would be on Floor 3 or Floor 4).
Since Floor 3 is occupied by N and Q, O must be on Floor 4 (meaning K is on Floor 2). Since L is at Floor 4, Flat 1, O must be at Floor 4, Flat 2.
M lives immediately below O, but not in the same named flat. Since O is at Floor 4, Flat 2, M must be at Floor 3, Flat 1. However, Floor 3, Flat 1 is already occupied by N. This creates a contradiction. Therefore, L cannot be on Floor 4.

Thus, L must live on Floor 2.

• L is at Floor 2, Flat 1.
• N lives on Floor 1, Flat 1 (immediately below L).
• Q lives on Floor 1, Flat 2 (east of N).

Step 3: Placement of J, K, O, M, and R
We can now place the remaining residents:

• One floor is between J's floor and L's floor. Since L is on Floor 2, J must be on Floor 4.
• Since L is in Flat 1 and K lives in a different named flat than L, K must live in Flat 2.
• Since K and R live in the same named flat, R must also live in Flat 2.
• K lives below O with one floor between them. The possible floors for K are Floor 2 or Floor 3. If K is on Floor 2, then O is on Floor 4.
• Let's place K at Floor 2, Flat 2. Since J and O are on Floor 4, one of them is in Flat 1 and the other is in Flat 2.
• M lives immediately below O, but not in the same named flat. If O is at Floor 4, Flat 2, then M must live at Floor 3, Flat 1. If O is at Floor 4, Flat 1, M must live at Floor 3, Flat 2.
• Since R must live in Flat 2, and the available positions in Flat 2 are on Floor 3 and Floor 4, let's place O at Floor 4, Flat 2. This leaves Floor 3, Flat 2 for R.
• M is placed at Floor 3, Flat 1 (immediately below O, not in the same flat).
• J is placed at Floor 4, Flat 1.

This configuration satisfies all the conditions perfectly.

Final Floor and Flat Chart:

Conclusion:
We need to find the number of persons living between S and N in the same numbered flat (Flat 1):
S is on Floor 5, Flat 1.
N is on Floor 1, Flat 1.
The persons living between them on Flat 1 are J (Floor 4), M (Floor 3), and L (Floor 2).
Therefore, there are exactly three persons living between S and N in the same flat.