Directions : Read the following information carefully and answer the following…

Concept

This is a facing-direction row puzzle: each house's gate opens north or south, alternating along the row (no two adjacent gates face the same way). Whenever a clue states a house is a certain number of positions ‘to the left/right of’ another house, that left/right must be read in the REFERENCE house's own facing direction — north-facing houses use the standard reading order, but a south-facing house has its own left and right mirrored (like two people facing each other). ‘Between’ and ‘near/adjacent’ clues, by contrast, are always plain physical distance and never flip.

Application

1. House D is 2nd from one of the ends, so D is at position 2 or position 10.

2. 'House P is fourth to the right of House D' is read in D's own frame. 'House D is immediate left of House R' is read in R's own frame. Testing D = 10 (south-facing, so D's own right points toward LOWER positions) places P at 10-4 = 6, with R (north-facing, standard frame) at 11 -- this keeps the initial D-P-R chain inside the row. D = 2 is ruled out once the remaining houses (Q, B, F) are placed, as the cross-check below confirms.

3. ‘Houses to the left of P’ (P's own frame; P faces south, so P's left is the HIGHER positions) = positions 7-11 = 5 houses. This must be one more than the houses between R(11) and P(6), i.e. positions 7-10 = 4 houses. 5 = 4 + 1, confirmed.

4. ‘Only two houses to the left of House A’ (A's own frame; A faces north, standard) fixes A at position 3.

5. Houses between P(6) and A(3) = positions 4-5 = 2. This is one less than houses between T and C, so that count is 3. House T is near (adjacent to) House P(6), so T is at position 5 or 7; only T = 5 leaves a valid slot exactly 4 away for C, giving C = 1.

6. 'House Q is immediate left of House B' is read in B's own frame. B faces south, so B's own left is the HIGHER-numbered side, placing Q one position above B (Q = B + 1). With F, Q, B, D, R still to fit into the remaining slots, this pins B = 8, Q = 9.

7. Only one house lies between F and Q, and both their gates face north (not south): with Q = 9 (north), F must also sit on a north-facing position exactly two away, giving F = 7.

8. The two positions left over, 2 and 4, must hold E and S with exactly one house between them (positions differ by 2) — satisfied either way — but House S is not near (not adjacent to) House C(1), which rules out S = 2. So S = 4 and E = 2.

9. The alternating gate pattern anchored by D(10)=south and R(11)=north extends uniquely across the row: positions 1,3,5,7,9,11 face north (C, A, T, F, Q, R) and 2,4,6,8,10 face south (E, S, P, B, D) — every one of the direction-sensitive clues above checks out against this pattern.

10. The question asks for houses to the right of House S — read in S's OWN frame. Since S faces south, S's own right is the LOWER-numbered side. Positions 1, 2 and 3 (Houses C, E and A) sit on that side, so exactly three houses are to the right of House S.

Cross-check

Re-reading every clue against the final row — C, E, A, S, T, P, F, B, Q, D, R (positions 1-11, gates N,S,N,S,N,S,N,S,N,S,N) — confirms all twelve conditions simultaneously (adjacency, betweenness, and every left/right relation in its reference house's own facing frame). No other placement of D (position 2 instead of 10) keeps the whole chain inside the 11-house row, so the arrangement, and therefore the count of three houses to House S's right, is unique.

Answer: Three.