Round Table Arrangement

This problem requires us to determine the seating position of friends around a circular table using given clues. We need to find who sits opposite friend D.

Constraints on Seating

Here are the conditions provided:

• Six friends: A, B, C, D, E, F.
• Setting: A round table.
• Clue 1: A is situated between E and F. This means the sequence along the circle is E-A-F or F-A-E.
• Clue 2: E is directly opposite D.
• Clue 3: C is not sitting next to E (on either side).

Visualizing Positions

Let's visualize the six seats around the table. We can number them 1 to 6 clockwise. If E is at position 1, then D must be at position 4 because they are opposite.

Seats 2 and 6 are adjacent to E. Seats 3 and 5 are adjacent to D.

E, A, F Sequence

From Clue 1, A is between E and F. This means A must be in a seat adjacent to E. Let's consider the two possibilities relative to E at seat 1:

1. Possibility 1 (E-A-F clockwise):
   • E is at seat 1.
   • A is at seat 2 (neighbor of E).
   • F is at seat 3 (neighbor of A, adjacent to D).
   Arrangement so far: E(1), A(2), F(3), D(4). Remaining seats are 5 and 6 for B and C. Seat 6 is adjacent to E.
2. Possibility 2 (F-A-E clockwise):
   • E is at seat 1.
   • A is at seat 6 (neighbor of E).
   • F is at seat 5 (neighbor of A, adjacent to D).
   Arrangement so far: E(1), D(4), F(5), A(6). Remaining seats are 2 and 3 for B and C. Seat 2 is adjacent to E.

C's Position Constraint

Now, let's apply Clue 3 (C is not on either side of E):

1. In Possibility 1: E(1), A(2), F(3), D(4). Seats 5 and 6 are left for B and C. Seat 6 is adjacent to E. Since C cannot be next to E, C cannot sit in seat 6. Thus, B must sit in seat 6, and C must sit in seat 5. The full arrangement is E, A, F, D, C, B (clockwise). Neighbors of E are A and B. C is not adjacent to E. This configuration is valid.
2. In Possibility 2: E(1), D(4), F(5), A(6). Seats 2 and 3 are left for B and C. Seat 2 is adjacent to E. Since C cannot be next to E, C cannot sit in seat 2. Thus, B must sit in seat 2, and C must sit in seat 3. The full arrangement is E, B, C, D, F, A (clockwise). Neighbors of E are B and A. C is not adjacent to E. This configuration is also valid.

Opposite D Finalized

In both valid arrangements derived from the clues:

• Arrangement 1: E, A, F, D, C, B (clockwise). D is at position 4. E is at position 1. E is opposite D.
• Arrangement 2: E, B, C, D, F, A (clockwise). D is at position 4. E is at position 1. E is opposite D.

Therefore, the person opposite D is consistently E.