Seven people, A, L, M, I, R, H and S, are sitting in a row, facing north.
No one sits to the right of S. Only three people sit between S and H. Only two people sit
between H and R. M sits third to the left of L. I sits to the immediate right of L.

How many people sit between A and R?

The correct option is Three.

Let us determine the step-by-step seating arrangement of the seven people (A, L, M, I, R, H, and S) sitting in a row facing north, numbered 1 to 7 from left to right:
_ _ _ _ _ _ _

Step 1: Position S and H
According to the clue, "No one sits to the right of S." This means S must be at the extreme right end, which is seat 7.
_ _ _ _ _ _ S (S is at position 7)
Next, "Only three people sit between S and H." Counting three places to the left from S (positions 6, 5, and 4), H must be placed at seat 3.
_ _ H _ _ _ S

Step 2: Position R
"Only two people sit between H and R." Since H is at position 3, we count two seats to its right (positions 4 and 5) and place R at position 6 (counting to the left is not possible as there are only two seats available to the left of H).
_ _ H _ _ R S

Step 3: Position L, M, and I
We are given two clues: "M sits third to the left of L" and "I sits to the immediate right of L."
If we place L at position 4:
- I, being to the immediate right of L, will be at position 5.
- M, being third to the left of L (position 4 - 3 = 1), will be at position 1.
This fits perfectly with the empty seats (1, 4, and 5) and does not overlap with existing occupied seats.
M _ H L I R S

Step 4: Position A
The only remaining empty position is seat 2, which must be occupied by A.
The final arrangement from left to right is:
M A H L I R S

Conclusion:
Now we count the number of people sitting between A (position 2) and R (position 6). The people sitting between them are H (position 3), L (position 4), and I (position 5).
Therefore, there are exactly three people sitting between A and R.