P, Q, R, S, T, U, V and W are sitting around a circle, facing the centre.…

Concept: In a circular arrangement where everyone faces the centre, seats are fixed one clue at a time by anchoring a reference person and placing the rest around them. Because the group faces inward, moving to a person's immediate right means moving anticlockwise around the circle. Two people are neighbours only when they occupy immediately adjacent seats, and each person has exactly two neighbours.

Application:

1. Fix T as the reference seat. Since T is the neighbour of both R and V, R and V must occupy the two seats immediately on either side of T.

2. P is second to the right of T (two seats away, moving anticlockwise, since the group faces the centre); this fixes P's seat.

3. V is the neighbour of U, so U must sit next to V. Of the two ways to place R and V beside T, only one lets U sit beside V without landing on a seat already taken by T or P; this fixes which side R is on and which side V is on, and seats U next to V.

4. With T, R, V, U and P now fixed, R sits between P and T on one side, while V sits between T and U on the other side — R and V are on opposite sides of T. This already settles the pair asked about (and also shows U-V and R-P are adjacent pairs), independent of exactly how the final three seats are filled.

5. The three remaining seats (for Q, S and W) are consecutive. 'S is not the neighbour of P' rules out one of those seats for S; one consistent way of satisfying 'Q is not between S and W' and 'W is not between U and S' seats them as S, then W, then Q.

Cross-check: with the full circle read in order — T, V, U, S, W, Q, P, R, back to T — every one of the five clues holds, and T also sits immediately to the right of V, matching the arrangement's own logic. Crucially, R and V's separation follows from clues (1)-(3) alone (step 4 above), so it does not depend on exactly how Q, S and W are seated among themselves.

Hence, R and V are the pair that are not neighbours.