Understanding the Circular Seating Arrangement Puzzle

This question asks us to determine the seating arrangement of eight girls around a circular table based on a set of clues and then verify two statements about their positions. All girls are facing the centre of the table. Let's break down the clues to build the arrangement step by step.

Analyzing the Clues for Seating Arrangement

We have eight girls: G1, G2, G3, G4, G5, G6, G7, and G8.

• G5 is third to the right of G1.
• G8 is second to the right of G4.
• G4 is not the immediate neighbour of G1 or G5.
• G6 and G2 are immediate neighbours.
• G2 is not the immediate neighbour of G1.
• G7 is not the immediate neighbour of G8.

Step-by-Step Construction of the Circular Arrangement

Let's start by placing G1 and use the clues to position others.

1. Place G1 anywhere on the circular table.
2. Place G5 third to the right of G1. In a circle of 8, this means there are two people between G1 and G5 when moving clockwise from G1 to G5.
3. Now consider G4 and G8. G8 is second to the right of G4. Also, G4 is not an immediate neighbour of G1 or G5. Immediate neighbours of G1 are the persons one position clockwise and one position anticlockwise from G1. Similarly for G5. Since G4 cannot be next to G1 or G5, this limits the possible positions for G4. Let's assume the positions are numbered 1 to 8 clockwise. If G1 is at position 1, G5 is at position 1 + 3 = 4 (clockwise). The neighbours of G1 are at 8 and 2. The neighbours of G5 are at 3 and 5. G4 cannot be at 8, 2, 3, or 5. So G4 must be at 6 or 7.
4. If G4 is at position 6, G8 is second to the right of G4 (at position 6 + 2 = 8). Let's check if this fits: G1(1), G5(4), G4(6), G8(8). G4(6) is not neighbour of G1(1) or G5(4). Yes, this is possible.
5. If G4 is at position 7, G8 is second to the right of G4 (at position 7 + 2 = 9, which is position 1 in a circle of 8). But G1 is at position 1. So G4 cannot be at position 7.
6. Thus, G4 is at position 6 and G8 is at position 8. Our arrangement so far (positions 1 to 8 clockwise): G1(_)(_)(G5)(_)(G4)(_)(G8). Positions 2, 3, 5, 7 are empty.
7. G6 and G2 are immediate neighbours. The only consecutive empty spots are positions 2 and 3. So, G6 and G2 must be at positions 2 and 3.
8. G2 is not the immediate neighbour of G1. G1 is at position 1. Its immediate neighbours are positions 8 and 2. Position 8 is occupied by G8. So, G2 cannot be at position 2.
9. If G2 is not at position 2, then G2 must be at position 3 (as G6 and G2 are neighbours at 2 and 3). This means G6 is at position 2.
10. Current arrangement: G1(1), G6(2), G2(3), G5(4), _(5), G4(6), _(7), G8(8). Positions 5 and 7 are empty. Girls left are G3 and G7.
11. G7 is not the immediate neighbour of G8. G8 is at position 8. Its immediate neighbours are positions 7 and 1. Position 1 is occupied by G1. So, G7 cannot be at position 7.
12. If G7 cannot be at position 7, it must be at the other empty position, which is 5.
13. The last remaining girl is G3, and the last empty position is 7. So, G3 is at position 7.

The final arrangement, clockwise from G1, is:

Reading clockwise around the table: G1 → G6 → G2 → G5 → G7 → G4 → G3 → G8 → G1.

Evaluating the Statements based on the Arrangement

Now let's check the given statements against our final seating arrangement.

Statement I Analysis: G7 is the immediate left of G4.

Immediate left, in a circular arrangement facing the centre, is the person sitting in the next position anticlockwise. In our clockwise arrangement: G1 → G6 → G2 → G5 → G7 → G4 → G3 → G8 → G1.

Find G4 in the arrangement. The person immediately to the left (anticlockwise) of G4 is G7.

Thus, Statement I is correct.

Statement II Analysis: G1 and G3 are neighbour of G8.

Neighbours of G8 are the persons sitting immediately on either side of G8. In our arrangement (clockwise): G1 → G6 → G2 → G5 → G7 → G4 → G3 → G8 → G1.

G8 is sitting between G3 and G1. Moving clockwise from G3 we reach G8, and moving clockwise from G8 we reach G1. This means G3 is immediately to the left of G8, and G1 is immediately to the right of G8. Both G1 and G3 are immediate neighbours of G8.

Thus, Statement II is correct.

Conclusion

Based on our step-by-step analysis of the clues and construction of the circular seating arrangement, we found that both Statement I ("G7 is the immediate left of G4") and Statement II ("G1 and G3 are neighbour of G8") are correct according to the final arrangement.

Revision Table: Key Positions in Seating Puzzle

Additional Information: Tips for Circular Arrangement Problems

Circular seating arrangement problems require careful deduction and step-by-step placement. Here are some general tips:

• Start with a Fixed Position: Although the table is circular, you can fix one person's position to start. All other positions are then relative to this person.
• Understand "Right" and "Left": When facing the centre, "right" is typically clockwise movement and "left" is anticlockwise movement.
• Identify Direct Placements: Clues like "X is third to the right of Y" allow you to place X relative to Y immediately.
• Use Negative Clues: Clues like "X is NOT a neighbour of Y" are crucial for eliminating possible positions and narrowing down options.
• Handle Neighbour Clues: Clues like "A and B are neighbours" mean A and B occupy adjacent seats. If one's position is known, the other is in one of the two seats next to them. If both are unknown but are neighbours, they occupy a pair of adjacent empty seats.
• Keep Track of Empty Seats: As you place people, keep track of which seats are still available.
• Verify All Clues: Once you arrive at a potential arrangement, quickly check if it satisfies *all* the given clues before answering the questions.