Analyzing the Seating Arrangement Puzzle

This problem requires us to figure out the exact positions of seven people (A, B, C, D, E, F, G) sitting in a single row. They are all facing north. Our main goal is to determine the final seating order and then count how many people are seated between individuals A and F.

Breaking Down the Clues

Let's list all the pieces of information given:

• There are a total of 7 people arranged in a row.
• Everyone is facing the North direction.
• Exactly five people are sitting between person F and person D.
• Person G is positioned third to the right of person F.
• Person E is sitting immediately next to both person C and person D.
• Person B is not sitting immediately next to person G.

Deducing the Arrangement Step-by-Step

Step 1: Determine the positions of F and D

With 7 seats in total, the condition "Only five people sit between F and D" strongly suggests that F and D must be occupying the two end seats. This creates a gap of 5 seats between them. There are two possibilities:

1. F is in the first seat (leftmost) and D is in the seventh seat (rightmost): F _ _ _ _ _ D.
2. D is in the first seat and F is in the seventh seat: D _ _ _ _ _ F.

Step 2: Position G relative to F

We are told that "G sits third to the right of F". Since they face North, "right" means moving towards the higher seat numbers.

• Let's examine the case D _ _ _ _ _ F. Here, F is in the 7th seat. There's no space to the right of F for G to sit. So, this case is not possible.
• Now, let's consider the case F _ _ _ _ _ D. F is in the 1st seat and D is in the 7th seat. G is third to the right of F. Counting from F (seat 1), the third seat to the right is seat 1 + 3 = 4. So, G is in the 4th seat. The arrangement now is: F _ _ G _ _ D.

Step 3: Place E and C based on adjacency

The clue "E is the immediate neighbour of C and D" is key here.

• We know D is in the 7th seat. Since E is D's immediate neighbour and it's a row, E must be in the 6th seat.
• E is also C's immediate neighbour. With E in the 6th seat, C must be in the 5th seat.
• The row now looks like this: F _ _ G C E D. We have filled seats 1, 4, 5, 6, and 7.

Step 4: Position the remaining people, A and B

The only people left to place are A and B. The empty seats are the 2nd and 3rd positions. This means A and B must occupy these two seats. There are two possible ways to arrange them:

1. Arrangement 1: F A B G C E D
2. Arrangement 2: F B A G C E D

Step 5: Use the final clue to finalize the order

The last condition is "B is not the immediate neighbour of G". G is in the 4th seat. The seats immediately next to G are the 3rd and 5th seats.

• In Arrangement 1 (F A B G C E D), B is in the 3rd seat. This seat is adjacent to G (4th seat). This arrangement violates the condition.
• In Arrangement 2 (F B A G C E D), B is in the 2nd seat. This seat is not next to G (4th seat). This arrangement satisfies all the given conditions.

Thus, the definitive seating arrangement from left to right (West to East, or position 1 to 7) is: F B A G C E D.

Calculating People Between A and F

We need to find how many people sit between A and F in the confirmed arrangement: F B A G C E D.

• F is located at the 1st position.
• A is located at the 3rd position.
• Looking at the positions between 1 and 3, we find only position 2.
• The person in position 2 is B.
• Therefore, there is exactly one person (B) sitting between A and F.