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A, B, C, D, P, Q, and R are sitting around a circular table, facing the centre (not necessarily in the same order). Only three people sit between D and R when counted from the right of R.B is an immediate neighbour of both R and Q.P sits second to the left of D.C is not an immediate neighbour of D. Who is sitting third to the right of R?
C
Q
A
P
A
Fix the reference point (R) at the top of the circle and map immediate neighbors first to limit possible placements quickly.
Fix the reference point (R) at the top of the circle and map immediate neighbors first to limit possible placements quickly.
Establish the base arrangement
With 7 seats in a circle, if we place R, the person 3 seats to the right of R (counting 1, 2, 3) is fixed. The constraint 'Only three people sit between D and R from the right of R' means if R is at position 1, D must be at position 5 (1+4=5). Counting right from R: R(1), 2, 3, 4, D(5).
Place neighbors and P
B is between R and Q. Since R is at 1, B must be at 7 (immediate neighbor of R). Q must be at 6 (immediate neighbor of B). P is second to the left of D. Since D is at 5, moving left (clockwise) 5 тЖТ 4 тЖТ 3, P is at 3.
Final positioning
The seats filled are: R(1), ?, P(3), ?, D(5), Q(6), B(7). The empty seats are 2 and 4. We have A and C left. C is not an immediate neighbor of D (seat 4), so C must be at seat 2. Therefore, A is at seat 4.
Verification
Arrangement clockwise: R, C, P, A, D, Q, B. Third to the right of R (1): move right to 2, 3, 4. The person at 4 is A.
B: Q is at position 6, not 4. C: C is at position 2, not 4. D: P is at position 3, not 4.
C is correct because A is sitting in the seat corresponding to the third position to the right of R in the verified circular arrangement.
In circular arrangements with an odd number of people, always check left/right directions carefully as they reverse compared to linear arrangements.