Nine persons – A, B, C, D, E, F, G, H, and I – are sitting around a circular table, all facing towards the center. But not necessarily in the same order.

Only one person sits between A and F. C sits third to the right B, who is an immediate neighbor of A. Only three people sit between A and G. G sits second to the left of H. I is an immediate neighbor of both A and H. F is not an immediate neighbor of D.

How many persons sit between G and E when counted from left of G?

The correct answer is One.

Let us solve the puzzle step-by-step by placing the nine persons (A, B, C, D, E, F, G, H, and I) around a circular table facing the center. Since everyone is facing the center, "right" refers to the counter-clockwise direction and "left" refers to the clockwise direction.

Step 1: Position A, I, and H
Let us place A at position 1.
According to the clue, "I is an immediate neighbor of both A and H." This means I must sit between A and H. There are two possibilities: I is to the immediate right of A (position 9) or to the immediate left of A (position 2).
We are also given: "G sits second to the left of H."
If we place I at position 9 (right of A) and H at position 8, then second to the left (clockwise) of H would be position 1 (which is already occupied by A). Thus, this case is invalid.
Therefore, we must place I at position 2 (left of A) and H at position 3 (left of I).

Step 2: Position G
"G sits second to the left of H."
Since H is at position 3, moving two places to the left (clockwise) puts G at position 5.
Let us verify the clue: "Only three people sit between A and G." Indeed, between A (position 1) and G (position 5) going clockwise, we have three people: I, H, and the person at position 4.

Step 3: Position B and C
"C sits third to the right of B, who is an immediate neighbor of A."
Since I is already at position 2, the other immediate neighbor of A must be B, which places B at position 9.
C sits third to the right (counter-clockwise) of B. Starting from B at position 9, moving three places counter-clockwise (9 ⇒ 8 ⇒ 7 ⇒ 6) places C at position 6.

Step 4: Position F
"Only one person sits between A and F."
With A at position 1, F must be at either position 3 or position 8. Since H is already at position 3, F must be placed at position 8.

Step 5: Position D and E
The remaining unoccupied seats are position 4 and position 7. The remaining persons to place are D and E.
We are given: "F is not an immediate neighbor of D."
Since F is at position 8, D cannot be at the adjacent position 7. Therefore, D must be at position 4, and E must be at position 7.

Final Seating Arrangement:
1: A
2: I
3: H
4: D
5: G
6: C
7: E
8: F
9: B

Answering the Question:
We need to find how many persons sit between G and E when counted from the left of G.
G is at position 5, and E is at position 7. Counting from the left (clockwise) of G (position 5), we move to position 6 (C) and then to position 7 (E).
There is exactly one person (C) sitting between G and E.