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.

What is the position of E with respect to A?

To find the position of E with respect to A, we can determine the arrangement step-by-step by placing the nine persons around a circular table facing the center.

Let us assume 9 positions numbered 1 to 9 in a clockwise order around the circle. Facing the center, going clockwise represents moving to the left, and going counter-clockwise represents moving to the right.

Step 1: Place A, I, and H
We are given that "I is an immediate neighbor of both A and H." This means the three people sit in a contiguous block as A - I - H or H - I - A.
Let us place A at position 1. Since I is next to A, I can be at position 2 or position 9.
Let's test if I is at position 2. Then H must be at position 3 (so that I is next to both A and H).
Now we check the condition: "G sits second to the left of H."
Since H is at position 3, moving second to the left (clockwise) leads to position 5. So, G is at position 5.
We are also given: "Only three people sit between A and G."
With A at position 1 and G at position 5, there are exactly three people (at positions 2, 3, and 4) between them in the clockwise direction. This perfectly satisfies the condition.

Step 2: Place F and B
"Only one person sits between A and F."
A is at position 1. The positions one seat away from A are position 3 and position 8. Since H is already at position 3, F must be at position 8.
"B is an immediate neighbor of A."
A is at position 1. The neighbors of A are positions 2 and 9. Since I is at position 2, B must be at position 9.

Step 3: Place C
"C sits third to the right of B."
B is at position 9. Facing the center at position 9, moving to the right (counter-clockwise) leads to position 8 (first right), position 7 (second right), and position 6 (third right). Therefore, C is at position 6.

Step 4: Place D and E
The remaining unoccupied positions are 4 and 7. The remaining people to be placed are D and E.
"F is not an immediate neighbor of D."
F is at position 8. Its immediate neighbors are positions 7 and 9. Since D cannot sit adjacent to F, D cannot be at position 7. Thus, D must be at position 4.
This leaves position 7 for E.

Summary of the final circular arrangement (clockwise from 1 to 9):
1: A
2: I
3: H
4: D
5: G
6: C
7: E
8: F
9: B

Step 5: Determine the position of E with respect to A
A is at position 1 and E is at position 7.
Facing the center from position 1 (A), going counter-clockwise (to the right):
First to the right is B (position 9)
Second to the right is F (position 8)
Third to the right is E (position 7)

Therefore, E sits Third to the right of A.