Statement I:
- B sits second to the right of D.
- D faces the centre.
- C sits to the immediate right of both B and D.
Since D is facing the centre, his right is the clockwise direction.
- B sitting second to the right of D means that there is one person between D and B.
- C sits to the immediate right of both B and D.
Let’s arrange them step by step:
- D is facing the center.
- B is second to the right → (D → X → B).
- C is immediately right of both B and D. Since C is right of D, it must sit immediately after D.
That means the arrangement so far is:
- D → C → X → B
- Only A remains, and A must be X.
So, the arrangement becomes:
D → C → A → B
Since D is facing the centre, we can now determine the direction of all others, and all of them are facing the centre.
Statement I alone is sufficient.
Statement II:
- A sits immediately left of B.
- C is not an immediate neighbour of A.
- C sits to the immediate right of D.
Step by step:
- C sits to the immediate right of D.
- A sits to the immediate left of B, meaning (A → B).
- C is not an immediate neighbour of A.
Let's assume D is facing the centre:
- If C is immediately right of D → (D → C)
- A cannot be next to C, so the only valid arrangement is:
- D → C → B → A.
Here, we can again confirm that all are facing the centre.
Statement II alone is sufficient.
Statement III:
- D is an immediate neighbour of both A and C.
- B sits to the immediate left of A.
- C sits to the immediate right of B.
Step by step:
- D is between A and C → (A → D → C or C → D → A).
- B is immediately left of A → (B → A).
- C is to the immediate right of B.
Combining:
- B is to the left of A, and C is to the right of B.
- So, the correct order is: B → A → D → C.
- If D is facing the centre, we can determine all others' positions, proving that all are facing the centre.
Statement III alone is sufficient.
Hence: Each statement alone is individually sufficient to determine that all four friends are facing the centre. Thus, the correct answer is:
Option 4: If the data in either Statement I alone or Statement II alone or Statement III alone are sufficient to answer the question.