Solving the Seating Arrangement Puzzle

This problem involves determining the exact seating positions of seven individuals (A, B, C, D, E, F, G) arranged in a single row facing north. We need to use the given clues to establish the order and then count the number of people situated between persons A and G.

Understanding the Conditions

• There are seven persons: A, B, C, D, E, F, G.
• They sit in a row facing north.
• F sits on the extreme left end.
• G sits second from one of the ends.
• E has an equal number of persons to his left and right.
• There are three persons between F and B.
• A sits immediate right of C (forming the pair 'CA').
• A does not sit at the corner.

Step-by-Step Arrangement Deduction

Let's represent the seven seats as slots: 1 2 3 4 5 6 7.

1. Positioning F: Condition 'F sits on the extreme left end' places F at position 1.
   Arrangement: F _ _ _ _ _ _
2. Positioning E: Condition 'E has equal number of persons to his left and right' means E must be in the center. For 7 positions, the center is the 4th position.
   Arrangement: F _ _ E _ _ _
3. Positioning B: Condition 'There are three persons between F and B'. Since F is at 1, there are 3 people at positions 2, 3, and 4. B must be at position 5.
   Arrangement: F _ _ E B _ _
4. Positioning G: Condition 'G sits second from one of the ends'. G can be at position 2 (second from left) or position 6 (second from right).

   Case 1 (G at pos 2): F G _ E B _ _. Remaining seats: 3, 6, 7. Remaining people: A, C, D.

   Case 2 (G at pos 6): F _ _ E B G _. Remaining seats: 2, 3, 7. Remaining people: A, C, D.

5. Positioning C and A: Condition 'A sits immediate right of C' means they must sit together as 'CA'.

   Evaluating Case 1: The remaining seats are 3, 6, 7. The pair 'CA' needs adjacent seats. The only adjacent seats are 6 and 7. If 'CA' occupy 6 and 7, the arrangement is F G _ E B C A. However, condition 'A does not sit at the corner' is violated as A is at position 7. Therefore, Case 1 is incorrect.

   Evaluating Case 2: The remaining seats are 2, 3, 7. The adjacent seats required for 'CA' are 2 and 3. This places C at 2 and A at 3.
   Arrangement: F C A E B G _

6. Checking A's Position: Condition 'A does not sit at the corner'. In Case 2, A is at position 3, which is not a corner. This case is valid.
7. Final Placement: The only person left is D, and the only seat left is position 7.
   Final Arrangement: F C A E B G D

Calculating Persons Between A and G

Now, let's find the number of people between A and G based on the final arrangement:

• Person A is at position 3.
• Person G is at position 6.
• The positions between A (3) and G (6) are 4 and 5.
• The persons occupying these positions are E and B.
• Therefore, there are two persons sitting between A and G.