Understanding the Square Table Seating Puzzle

This puzzle involves arranging seven friends (A, B, C, D, E, F, and G) around a square table. There are eight available positions: four at the corners and four at the exact centres of the sides. One position is left vacant. All individuals are facing towards the centre of the table, which is crucial for determining left and right.

Breaking Down the Clues

We are given several clues about the relative positions of the friends:

• D is sitting exactly at the centre of one of the sides.
• C is sitting at a corner, third to the left of B.
• There are exactly two people sitting between C and D.
• F is an immediate neighbour of both B and D.
• A is second to the right of F.
• E is not an immediate neighbour of A, but third to the left of F.
• G is an immediate neighbour of C.

Our goal is to use these clues to determine the position of each person and identify the vacant seat.

Step-by-Step Deduction Process

Let's deduce the seating arrangement step-by-step:

1. We start with a definite position. D is at a side centre. Let's assume, for instance, D is at the top side centre.
2. F is an immediate neighbour of both B and D. Since D is at a side centre, its neighbours must be at the adjacent corners. So, F must be at one of the corners next to D. As F is also a neighbour of B, and F is at a corner, its neighbours are the adjacent side centre (which is D) and the adjacent corner. Therefore, B must be at the corner adjacent to F on the other side from D. This implies a sequence of Side Centre (D) - Corner (F) - Corner (B). Let's place D at the top side centre, F at the top-left corner, and B at the left side centre. (Note: Placing F at the top-right corner and B at the right side centre would also be a valid starting point and lead to the same relative arrangement).
3. C is sitting at a corner, third to the left of B. B is at the left side centre. Moving left from B: the first position is the bottom-left corner, the second is the bottom side centre, and the third is the bottom-right corner. So, C is at the bottom-right corner. This position is indeed a corner, as stated in the clue.
4. There are exactly two people sitting between C and D. We have C at the bottom-right corner and D at the top side centre. Looking at the positions between them, moving anti-clockwise from C (bottom-right corner) towards D (top side centre), we find the right side centre and the top-right corner. There are two positions between them. This confirms our placement so far.
5. A is second to the right of F. F is at the top-left corner. Moving right from F: the first position is the top side centre (occupied by D), and the second position is the top-right corner. So, A is at the top-right corner.
6. E is not an immediate neighbour of A, but third to the left of F. F is at the top-left corner. Moving left from F: the first position is the left side centre (occupied by B), the second position is the bottom-left corner, and the third position is the bottom side centre. So, E is at the bottom side centre. Let's check the condition that E is not a neighbour of A. A is at the top-right corner. Its neighbours are the top side centre (D) and the right side centre. E is at the bottom side centre, which is not adjacent to A. This condition holds true.
7. G is an immediate neighbour of C. C is at the bottom-right corner. Its neighbours are the bottom side centre (occupied by E) and the right side centre. Since E is already placed, G must be at the right side centre.

Final Seating Arrangement

Based on our deductions, we can map each person to a specific position around the square table. There are 8 positions in total, and 7 are occupied by friends.

The positions occupied are by A, B, C, D, E, F, and G. The only position that is not occupied is the Bottom-Left Corner.

Identifying the Vacant Seat Location

The vacant seat is at the Bottom-Left Corner position. Now let's compare this with the given options:

• Option 1: Third to the right of C. C is at the Bottom-Right Corner. Counting right from C: E (1st right), Vacant (2nd right), B (3rd right). The third position to the right of C is occupied by B. This is incorrect.
• Option 2: To the immediate left of B. B is at the Left Side Centre. The position immediately to the left of B is the Bottom-Left Corner. This is the position of the vacant seat. This is correct.
• Option 3: To the immediate left of E. E is at the Bottom Side Centre. The position immediately to the left of E is the Bottom-Right Corner, occupied by C. This is incorrect.
• Option 4: Third to the right of D. D is at the Top Side Centre. Counting right from D: A (1st right), G (2nd right), C (3rd right). The third position to the right of D is occupied by C. This is incorrect.

Conclusion

Based on the step-by-step deduction and verification of the options, the vacant seat is located immediately to the left of B.

Revision Table: Key Puzzle Concepts

Additional Information: Strategies for Seating Puzzles

Solving seating arrangement puzzles requires careful reading and systematic deduction. Here are some helpful strategies:

• Always start with a definite or relatively fixed piece of information (like a person at a specific type of position, e.g., corner or side centre).
• Draw a diagram of the seating arrangement (a circle or square with slots) and fill it in as you deduce positions.
• Use all the clues. Make sure your final arrangement satisfies every condition given in the puzzle.
• Pay close attention to directional terms (left/right) and distances (immediate, second, third, etc.). Remember directions are relative to the person facing the centre.
• Use negative information (e.g., "E is not a neighbour of A") to eliminate possibilities.
• If a clue can be interpreted in multiple ways, explore one possibility first. If it leads to a contradiction with other clues, backtrack and try the other possibility.