Circular Arrangement Puzzle: Solving for R's Left Neighbour

This problem involves a logical reasoning puzzle about the seating arrangement of seven girls (P, Q, R, S, T, U, V) around a circular table. A key detail is that they are all facing opposite to the centre of the table. Our goal is to find out who sits immediately to the left of R.

Analyzing the Seating Clues

Let's break down the information provided:

• Clue 1: P is the immediate neighbour of both Q and R. This means P sits exactly between Q and R, forming a block like Q-P-R or R-P-Q.
• Clue 2: V is the immediate neighbour of both T and U. This means V sits exactly between T and U, forming a block like T-V-U or U-V-T.
• Clue 3: S is the immediate neighbour of U. This means S and U are sitting next to each other (S-U or U-S).
• Clue 4: V is second to the right of S. Since they face opposite the centre, we need to be careful with directions. Let's assume positions are numbered clockwise around the table. If S is at position 1, their right is position 2, and the second position to their right is position 3. So, V is two spots away clockwise from S.
• Clue 5: S is not the immediate neighbour of either R or T. This is a constraint to verify our final arrangement.

Deriving the Arrangement Step-by-Step

Let's combine the clues to figure out the seating order:

1. From Clue 3 (S neighbours U) and Clue 2 (V neighbours T and U), we can deduce a sequence. Since V must be between T and U, and S must be next to U, the sequence must involve S connected to the T-V-U block. This leads to a block of four people: S-U-V-T (assuming U is between S and V). Let's check if the other order works: if the block is U-V-T, and S neighbours U, we still get S-U-V-T.
2. Now let's use Clue 4: V is second to the right of S. Let's place S at a reference point (say, the top position). Moving clockwise (which represents 'right' for someone facing opposite the centre), the order would be: S (position 1), U (position 2), V (position 3). This confirms the S-U-V-T sequence in clockwise order.
3. We have accounted for S, U, V, and T. The remaining girls are P, Q, and R. They must fill the remaining three spots.
4. From Clue 1, P, Q, and R form a block (Q-P-R or R-P-Q). This block must fit into the remaining three consecutive seats.
5. Combining the S-U-V-T sequence and the PQR block, the full circle arrangement (clockwise) must be: S, U, V, T, R, P, Q.
6. Let's verify with Clue 5: S is not the neighbour of R or T. In our arrangement (S, U, V, T, R, P, Q), S's neighbours are Q (counter-clockwise) and U (clockwise). This satisfies the condition.

Visualizing the Final Arrangement

The clockwise seating order is:

• Seat 1: S
• Seat 2: U
• Seat 3: V
• Seat 4: T
• Seat 5: R
• Seat 6: P
• Seat 7: Q

Remember, everyone is facing *opposite* the centre.

Identifying R's Immediate Left Neighbour

We need to find who is sitting on R's immediate left.

• R is sitting at Seat 5.
• The person clockwise to R (Seat 6) is P. This is on R's right side, as they face outwards.
• The person counter-clockwise to R (Seat 4) is T. This is on R's left side, as they face outwards.

Therefore, T is sitting on the immediate left of R.

Conclusion

Based on the step-by-step deduction from the given clues, T is the person sitting on the immediate left of R.