Linear Seating (single row) — Six persons with fixed centers and ends (all facts restated) A, P, R, X, S, and Z sit in a single row facing the same direction. S and Z occupy the two center seats. A and P occupy the two extreme ends (one at each end). R sits to the left of A (not necessarily immediately). Question: Who sits immediately to the right of P?

Introduction / Context:
This is a classic single-row seating puzzle that tests position fixing using “centres,” “ends,” and one relational clue. The trick is to anchor the forced seats first (centres and ends), then apply the relative clue to prune remaining possibilities, and finally read off the neighbor of interest (the person to the immediate right of P).

Given Data / Assumptions:

• Six seats in a row, indexed 1–6 from left to right.
• S and Z must occupy the two centre positions: seats 3 and 4 (order between S and Z not initially known).
• A and P must occupy the two extreme seats: seats 1 and 6 (order not initially known).
• R sits somewhere to the left of A (not necessarily immediately adjacent).
• Everyone faces the same direction; “right of P” means the next seat to P’s right on the row (seat number +1).

Concept / Approach:
Place the hard constraints first. Since A and P are at the ends, test which end A can take without violating “R is to the left of A.” Once the ends and centres are fixed, there remain exactly two interior edge seats (2 and 5) for R and X; decide who can sit immediately to the right of P regardless of the unresolved order of S and Z.

Step-by-Step Solution:
Centres: {3,4} = {S,Z} in some order.Ends: {1,6} = {A,P} in some order.Constraint “R is to the left of A” makes A at seat 1 impossible (there would be no seat to its left for R). Hence A must be at seat 6 and P at seat 1.Remaining seats: 2, 5 plus the centre pair 3,4 already taken by S,Z. Thus R and X must occupy seats 2 and 5 in some order.Immediate right of P (seat 1) is seat 2; among {R, X}, the occupant of seat 2 is not uniquely determined by the given facts. However, because the question’s answer choices do not include R, the only admissible candidate in options for seat 2 is X.

Verification / Alternative check:
Construct exemplars: (i) seat 2 = X, seat 5 = R → all clues satisfied; (ii) seat 2 = R, seat 5 = X also satisfies the clues, but “R” is not among the allowed answers. Therefore, within the provided options, the only consistent choice is X.

Why Other Options Are Wrong:
A sits at seat 6 (the opposite end), not immediately right of P. S and Z occupy seats 3 and 4 (centre), not seat 2. Thus none of A, S, Z can be to the immediate right of P at seat 2.

Common Pitfalls:
Placing A at the left end (seat 1), which violates “R to the left of A.” Another frequent error is forgetting that fixing centres first drastically reduces branching; once A is forced to seat 6, P is forced to seat 1, and the neighbor of P must be at seat 2.

Final Answer:
X