Step-by-step Solution:

Quick Solution

This is a linear arrangement puzzle. We can solve it by drawing out the seven positions in the line and filling them in step-by-step using the clues. Since all are facing East, we can consider one end of the line as North and the other as South.

1. Step-by-Step Arrangement

1. Let's set up the 7 positions, with 1 being the North end and 7 being the South end.
   (North) 1-2-3-4-5-6-7 (South)
2. The most definite clue is "D is sitting third from the south end". Counting from position 7 (South), this places D at position 5.
3. Next, "C is immediate to the right of D". Since they are facing East, D's right is the next spot towards the South. This places C at position 6.
4. The clues "B is at one of the extreme ends" and "has E as his neighbour" determine B's position. If B were at the South end (7), his neighbour (at 6) would be C, not E. Therefore, B must be at the North end. This places B at position 1 and E at position 2.
5. Our line now looks like this:
   
   B E _ _ D C _
6. Finally, "G is between E and F". Since E is at position 2, the only way for G to be between E and F is if the order is E-G-F. This places G at position 3 and F at position 4.
7. The only person left is A, who must take the last empty spot at position 7.

2. The Final Arrangement

The complete arrangement from the North end to the South end is:

3. Answering the Question

The question asks who is sitting at the two extreme ends of the line.

• The person at the North end is B.
• The person at the South end is A.

Final Answer: The persons sitting at the extreme ends are A & B.