Eight friends A, B, C, D, E, F, G, and H are seated around a circular table, not necessarily in the given order. Exactly four of them face outward, and the other four face the center. E faces outward. Both neighbors of E face the center. H is seated second to the right of E. B is seated third to the left of E. How many people are seated between A and C when counted clockwise from A?

I. G is seated second to the left of A. B is seated third to the right of H, and D is not an immediate neighbor of B.

II. F is an immediate neighbor of D. C is an immediate neighbor of G.

Based on the above statements, choose the correct option:

Question

Eight friends A, B, C, D, E, F, G, and H are seated around a circular table, not necessarily in the given order. Exactly four of them face outward, and the other four face the center. E faces outward. Both neighbors of E face the center. H is seated second to the right of E. B is seated third to the left of E. How many people are seated between A and C when counted clockwise from A?

I. G is seated second to the left of A. B is seated third to the right of H, and D is not an immediate neighbor of B.

II. F is an immediate neighbor of D. C is an immediate neighbor of G.

Based on the above statements, choose the correct option:

Accepted Answer

**Solution:**

1. From the question, we know:
   - Eight friends A, B, C, D, E, F, G, H sit in a circle.
   - Four face outside, four face inside.
   - E faces outside.
   - Both neighbors of E face inside.
   - H is second to the right of E.
   - B is third to the left of E.

2. Statement I adds:
   - G is second to the left of A.
   - B is third to the right of H.
   - D is not an immediate neighbor of B.

3. Statement II adds:
   - F is an immediate neighbor of D.
   - C is an immediate neighbor of G.

4. Using the given information and statements together, we can arrange the friends around the circle respecting the directions they face and their relative positions.

5. After placing E and neighbors, and using the positions of H and B relative to E, and then incorporating the neighbors of A, B, C, D, F, and G from statements I and II, the seating order can be deduced.

6. From the final arrangement, counting clockwise from A to C, there are exactly two people seated between them.

**Answer:** Both statements I and II together are sufficient to answer the question.

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