Seven people P, Q, R, S, T, U and V are sitting around a circular table facing…

In a circular seating puzzle where everyone faces the centre, every "X sits nth to the left/right of Y" clue is a fixed directional offset from Y along the circle. Fixing one person as the reference seat and applying each offset in a single consistent rotational direction places every other person; the seats immediately before and after the person asked about then give its immediate neighbours.

Application

1. Fix P at seat 1 of the 7 circular seats, numbered 1 to 7 in the direction that corresponds to a seated person's left (since everyone faces the centre, moving to a person's right goes the opposite way around the same numbering).

2. T sits immediately to the left of P, so T takes seat 2 (1 + 1).

3. U sits third to the left of P, so U takes seat 4 (1 + 3).

4. S sits second to the left of U, so S takes seat 6 (4 + 2).

5. S sits immediately to the right of R, so R is one seat further in the left direction than S, taking seat 7 (6 + 1).

6. R sits third to the right of V, so V is three seats further in the left direction than R: 7 + 3 = 10, which wraps around the 7-seat circle to seat 3.

7. Seats 1 to 7 are now P, T, V, U, blank, S, R, with only seat 5 left empty, so Q takes seat 5.

Cross-check

• T immediately left of P: seat 2 minus seat 1 equals 1.

• U third to the left of P: seat 4 minus seat 1 equals 3.

• S second to the left of U: seat 6 minus seat 4 equals 2.

• S immediately to the right of R: from seat 7 (R), one step right lands on seat 6 (S).

• R third to the right of V: from seat 3 (V), three steps right lands on seat 7 (R), wrapping the same way the arrangement was built.

• Every one of the five original clues holds in this final order, and it is the only order consistent with all of them together.

With Q fixed at seat 5, the seats on either side of it are seat 4 (U) and seat 6 (S). So the immediate neighbours of Q are U and S.