Eight persons A, B, C, D, E, F, G, and H are sitting around a circular table. All of them are facing the center. Two persons are sitting between B and D. F is sitting 2nd to the left of D. One person is sitting between F and C. G is sitting 2nd to the left of A, who is not an immediate neighbor of F. H is not sitting adjacent to B. Neither H nor E is sitting opposite to G. Two persons are not sitting between G and F, when counted from the left of G.

To determine the seating arrangement of the eight persons around the circular table based on the given conditions, we can start by noting the positions step by step:

1. **Initial Setup:**
   - Let’s place \( B \) and \( D \) with two persons between them. Since it’s a circular table, there are two possible setups for \( B \) and \( D \):

     - \( B \) - _ - _ - \( D \)
     - \( D \) - _ - _ - \( B \)

2. **F’s Position Relative to D:**
   - \( F \) is sitting 2nd to the left of \( D \). So, if \( D \) is at position 1, then \( F \) would be at position 7.

     - \( D \) - _ - _ - _ - _ - _ - \( F \)
   
   - If \( D \) is at position 3, then \( F \) would be at position 1.

     - _ - _ - \( D \) - _ - _ - _ - \( F \)

3. **One Person Between F and C:**
   - If \( F \) is at position 7 and one person is between \( F \) and \( C \):

     - \( D \) - _ - _ - _ - _ - _ - \( F \) - _ - \( C \)
   
   - If \( F \) is at position 1 and one person is between \( F \) and \( C \):

     - \( C \) - _ - \( D \) - _ - _ - _ - \( F \)

4. **G’s Position Relative to A:**
   - \( G \) is sitting 2nd to the left of \( A \).

5. **A is Not an Immediate Neighbor of F:**
   - If \( F \) is at position 7, \( A \) could be at position 5 or 9 (which is equivalent to position 1).
   - If \( F \) is at position 1, \( A \) could be at position 8 or 3 (which is \( D \)).

6. **H’s Position Relative to B:**
   - \( H \) is not sitting adjacent to \( B \).

7. **Neither H Nor E is Opposite to G:**

8. **Two Persons Not Sitting Between G and F, Counted From the Left of G:**

Using these constraints, we can place each person step by step.

Let’s place \( D \) and \( F \) first:
- \( D \) at position 1, \( F \) at position 7:

\[ (1) D - (2) - (3) - (4) - (5) - (6) - (7) F \]

Next, we place \( C \):
- \( F \) at position 7, one person between \( F \) and \( C \):

\[ (1) D - (2) - (3) - (4) - (5) - (6) - (7) F - (8) - (9) C \]
(Note that position 9 is equivalent to position 1, so position 8 for \( C \)).

\[ (1) D - (2) - (3) - (4) - (5) - (6) - (7) F - (8) C \]

Next, \( A \) and \( G \):
- \( A \) should not be immediate neighbor of \( F \) and \( G \) is 2nd to the left of \( A \):
- Suppose \( A \) at position 5, \( G \) would be at position 3.

\[ (1) D - (2) - (3) G - (4) - (5) A - (6) - (7) F - (8) C \]

- This doesn’t violate any conditions yet. 

Now let’s place \( B \):
- \( B \) and \( D \) have two persons between them:

\[ (1) D - (2) - (3) G - (4) B - (5) A - (6) - (7) F - (8) C \]

Finally, \( H \) and \( E \):
- \( H \) is not adjacent to \( B \) and neither \( H \) nor \( E \) are opposite \( G \):

So \( H \) can be at position 6 and \( E \) at position 2.

Final arrangement:
\[ (1) D - (2) E - (3) G - (4) B - (5) A - (6) H - (7) F - (8) C \]

This satisfies all the given conditions.

Would you like any specific details or have any questions?

Here are five more questions you might want to ask:
1. Can you explain how you determined the positions of \( G \) and \( A \)?
2. What would be a different possible arrangement if there is any?
3. Can you provide a step-by-step explanation for each constraint?
4. How do the conditions “not sitting opposite” affect the arrangement?
5. Can you show the reasoning for placing \( H \) and \( E \) last?

**Tip:** When solving seating arrangement problems, drawing a diagram and labeling the positions can be very helpful.

Explore how to solve a complex circular seating arrangement problem involving constraints. This problem includes arranging eight persons around a circular table with specific conditions such as relative positions, non-adjacency, and opposite seating restrictions.

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