M, N, O, P, Q, and R are sitting around a circular table facing the center. M sits second to the left of R. Only one person sits between R and Q. O is not the immediate neighbor of M. N sits third to the right of Q. How many people sit between Q and R, when counted from the right of R?
M, N, O, P, Q, and R are sitting around a circular table facing the center. M sits second to the left of R. Only one person sits between R and Q. O is not the immediate neighbor of M. N sits third to the right of Q. How many people sit between Q and R, when counted from the right of R?
Solution
When everyone faces the center, moving to a person's left means moving clockwise, and moving to the right means anticlockwise.
Number the seats to clockwise and place R at seat .
M sits second to the left of R: seats clockwise, so M is at seat .
Only one person sits between R and Q: Q is at seat or seat . Seat is taken by M, so Q is at seat .
N sits third to the right of Q: seats anticlockwise from seat gives seat .
So N is at seat .
Seats and are left for O and P.
Seat is next to M (seat ), and O is not M's neighbour, so O is at seat and P is at seat .
Clockwise order: R, N, M, P, Q, O
Counting from the right of R (anticlockwise): O, then Q.
Only O sits between R and Q.
Therefore, person sits between Q and R.
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