How many persons sit between M and S? Study the following information carefully and answer the questions given below:
Seven persons -M, N, O, P, Q, R and S sit in a linear row and facing the north but not necessarily in the same order.
Only four persons sit between P and Q who does not sit at the extreme end of the row. S sits to the immediate right of Q. The number of persons sitting to the right of S is same as the number of persons sitting between M and N who sits to the immediate left of R. O sits to the left of R.

To find the number of persons sitting between M and S, let us analyze the given clues step-by-step and determine the linear arrangement of the seven persons (M, N, O, P, Q, R, and S) facing North.

Step 1: Position P and Q
- Clue: "Only four persons sit between P and Q who does not sit at the extreme end of the row."
- Since there are 7 positions in total (let's number them 1 to 7 from left to right), a gap of 4 persons means P and Q are separated by 5 places (i.e., if one is at position x, the other is at x + 5).
- Q cannot be at the extreme ends (position 1 or 7). Therefore, we have two possible cases:
  • Case 1: Q is at position 2, and P is at position 7.
  • Case 2: P is at position 1, and Q is at position 6.

Step 2: Position S
- Clue: "S sits to the immediate right of Q."
  • In Case 1 (Q at 2): S must be at position 3. The arrangement becomes: _ , Q , S , _ , _ , _ , P
  • In Case 2 (Q at 6): S must be at position 7. The arrangement becomes: P , _ , _ , _ , _ , Q , S

Step 3: Analyze the relationship between S, M, N, and R
- Clue: "The number of persons sitting to the right of S is same as the number of persons sitting between M and N who sits to the immediate left of R."
- Let's test both cases with this clue:
  • In Case 1: S is at position 3, so there are 4 persons sitting to the right of S (positions 4, 5, 6, 7). This means there must be 4 persons between M and N. Since N sits immediately to the left of R (represented as NR), placing M and NR with a gap of 4 in the remaining positions is impossible. Thus, Case 1 is eliminated.
  • In Case 2: S is at position 7, so there are 0 persons sitting to the right of S. This means there are 0 persons between M and N, indicating that M and N sit adjacent to each other. Since N sits to the immediate left of R, we have the adjacent group as M , N , R.

Step 4: Place the remaining persons
- In Case 2, the current row is: P , _ , _ , _ , _ , Q , S (empty positions are 2, 3, 4, 5).
- We need to place the consecutive group M , N , R and the remaining person O.
- Clue: "O sits to the left of R."
- If we place M, N, and R at positions 3, 4, and 5 respectively, then O must sit at position 2. This satisfies the condition that O (at position 2) sits to the left of R (at position 5).
- The final valid seating arrangement from left to right is:
P (1) - O (2) - M (3) - N (4) - R (5) - Q (6) - S (7)

Conclusion:
- M is at position 3 and S is at position 7.
- The persons sitting between M and S are N, R, and Q.
- Therefore, there are exactly three persons sitting between M and S.