This problem involves a logical reasoning puzzle where we need to determine the seating arrangement of 7 people around a circular table based on given clues and then answer a specific question about the arrangement.

Understanding the Constraints

We have 7 people: A, B, L, M, S, T, and Z, all sitting around a circular table facing the center. Let's break down the clues:

• Clue 1: Only four people sit between M and T when counted from the right of M.
• Clue 2: M sits third to the left of L.
• Clue 3: S sits third to the left of Z.
• Clue 4: B is an immediate neighbour of both T and L.

Step-by-Step Arrangement

Let's denote the positions around the table as 1, 2, 3, 4, 5, 6, 7 in a clockwise direction.

1. Using Clue 1: "Only four people sit between M and T when counted from the right of M." If we start at M and move clockwise (to the right), we count four people, and the next person is T. This means M and T are separated by 4 people in one direction and 1 person in the other direction. Let's place M at position 1. Moving right (clockwise): M (pos 1), Person 1, Person 2, Person 3, Person 4, T (pos 6). So, T is at position 6. The arrangement looks like: M, _, _, _, _, T, _. (Positions: 1=M, 2=?, 3=?, 4=?, 5=?, 6=T, 7=?).
2. Using Clue 2: "M sits third to the left of L." Since they face the center, 'left' means counter-clockwise. So, L is third clockwise from M. Starting from M (pos 1): M (pos 1), pos 2, pos 3, L (pos 4). Thus, L is at position 4. The arrangement is now: M, _, _, L, _, T, _. (Positions: 1=M, 2=?, 3=?, 4=L, 5=?, 6=T, 7=?).
3. Using Clue 4: "B is an immediate neighbour of both T and L." L is at position 4 and T is at position 6. The neighbours of L are positions 3 and 5. The neighbours of T are positions 5 and 7. The common neighbour is position 5. Therefore, B must be at position 5. The arrangement is: M, _, _, L, B, T, _. (Positions: 1=M, 2=?, 3=?, 4=L, 5=B, 6=T, 7=?).
4. Using Clue 3: "S sits third to the left of Z." This means Z is third clockwise from S (S, Person 1, Person 2, Z). We have empty seats at positions 2, 3, and 7. Let's test the possibilities for S and Z:
   • If S is at 2, Z would be at 5. But B is at 5. Not possible.
   • If S is at 3, Z would be at 6. But T is at 6. Not possible.
   • If S is at 7, Z would be at 3. (Counter-clockwise from Z (pos 3): pos 2, pos 1, pos 7. So Z is third clockwise from S). This fits!
   So, S is at position 7 and Z is at position 3. The arrangement is: M, _, Z, L, B, T, S. (Positions: 1=M, 2=?, 3=Z, 4=L, 5=B, 6=T, 7=S).
5. Placing the last person: The only remaining person is A, and the only remaining seat is position 2.

Final Seating Arrangement

The final arrangement clockwise is: M, A, Z, L, B, T, S.

Positions:

• Position 1: M
• Position 2: A
• Position 3: Z
• Position 4: L
• Position 5: B
• Position 6: T
• Position 7: S

Answering the Question

The question asks: "How many people sit between A and B when counted from the right of A?"

• A is at position 2.
• B is at position 5.
• Counting from the right (clockwise) of A:
• A (pos 2) -> Z (pos 3) -> L (pos 4) -> B (pos 5).
• The people between A and B in this direction are Z and L.
• There are 2 people between A and B when counted from the right of A.