Circular Table Seating Arrangement Solution

This problem involves determining the seating positions of six people (A, B, C, D, E, F) around a circular table based on relative positions and then finding the number of people between two specific individuals (E and B).

Applying Seating Constraints

We assume 6 seats around the table, numbered 1 to 6 clockwise. Facing the center, "right" means clockwise and "left" means counter-clockwise.

• Constraint 1: B sits third to the right of C. (If C is at seat 1, B is at seat 4).
• Constraint 2: C sits second to the left of A. (This means A is second to the right of C. If C is at seat 1, A is at seat 3).
• Constraint 3: F sits third to the right of D.
• Constraint 4: D sits to the immediate left of E. (They are adjacent, DE counter-clockwise or ED clockwise).

Deducing the Arrangement

1. Place C at seat 1.
2. From Constraint 1, B is 3 seats to the right of C. Seats: C (1), Seat 2, Seat 3, B (4).
3. From Constraint 2, A is 2 seats to the right of C. Seats: C (1), Seat 2, A (3), B (4).
4. The remaining seats are 2, 5, and 6. The people left are D, E, and F.
5. Constraint 4 states D is immediately left of E. They must occupy adjacent seats. The only available adjacent pairs are (5, 6). So, D must be at seat 5 and E at seat 6.
6. This leaves seat 2 for F.
7. Final Arrangement (Clockwise): C (1), F (2), A (3), B (4), D (5), E (6).
8. Verify Constraint 3: F sits third to the right of D. D is at seat 5. Counting right: Seat 6 (E), Seat 1 (C), Seat 2 (F). This matches.

Calculating People Between E and B

The question asks for the number of people between E and B, counted from E's left.

• E is at seat 6.
• B is at seat 4.
• Counting from E's left (counter-clockwise):
• The first person to E's left is D (at seat 5).
• The next person is B (at seat 4).
• The sequence is E -> D -> B.
• The only person sitting between E and B in this direction is D.

Therefore, there is one person between E and B when counted from E's left.