Problem:


Seven friends - A, B, C, D, E, F, and G are sitting around a circular table facing towards the center. F is second to the right of B and is a neighbor of F, but not of C. E is the neighbor of C and sitting fourth to the right of G. D is sitting between E and A. We need to determine the seating arrangement of the seven friends.

Solution:

Step 1: Understand the given information

- There are seven friends - A, B, C, D, E, F, and G.
- They are sitting around a circular table facing towards the center.
- F is second to the right of B.
- F is a neighbor of F, but not of C.
- E is the neighbor of C.
- E is sitting fourth to the right of G.
- D is sitting between E and A.

Step 2: Represent the seating arrangement

To solve the problem, let's represent the seating arrangement using a circle. We can label the positions around the circle as 1, 2, 3, 4, 5, 6, and 7 in a clockwise manner. Each position represents a friend sitting at that place.

Our circle representation looks like this:

```
1
7 2
6
5 3
4
```

Step 3: Analyze the given information

From the given information, we can infer the following:

1. F is second to the right of B.
- This means F is sitting at position 4.

2. F is a neighbor of F, but not of C.
- Since F is sitting at position 4, F cannot be a neighbor of C.
- Therefore, F is not sitting at positions 3 or 5.
- Hence, F is sitting at either position 2 or 6.

3. E is the neighbor of C.
- Since E is a neighbor of C, E cannot be sitting at positions 1 or 7.
- Therefore, E is sitting at either position 2, 3, 4, 5, or 6.

4. E is sitting fourth to the right of G.
- Since E is sitting fourth to the right of G, G must be sitting at position 3 or 7.
- If G is sitting at position 3, then E must be sitting at position 7, which contradicts with the previous inference.
- Therefore, G is sitting at position 7 and E is sitting at position 3.

5. D is sitting between E and A.
- Since E is sitting at position 3, A cannot be sitting at positions 2 or 4.
- Therefore, A is sitting at either position 1, 5, or 6.
- Since D is sitting between E and A, D must be sitting at position 2 or 4.

Step 4: Determine the seating arrangement

Using the given information and the inferences made, we can determine the seating arrangement as follows:

- G is sitting at position 7.
- E is sitting at position 3.
- A is sitting at position 6.
- D is sitting at position 2