Circular Arrangement

At a glance 9 rules

1. 1Facing the centreRight is anticlockwise and left is clockwise. To check, turn the page so the person sits at the bottom facing up: their right is then your right.
2. 2Facing outward flips itFacing out, right is clockwise. If all face the same way, left is one direction for everyone; at a mixed table, arrow each seat and read each clue from that person.
3. 3Pin one personA circle has no first seat, so fix the most-mentioned person at the top. Turning the whole table never changes an answer.
4. 4Opposite: half a lapWith $n$ seats, opposite is $\tfrac{n}{2}$ seats away either way, so it exists only when $n$ is even: at a 7-seat table nobody sits directly opposite.
5. 5One seat, two countsWith $n$ seats, $k$th to the left is $(n - k)$th to the right. So if X is $a$th to the left and $b$th to the right of the same person, $n = a + b$.
6. 6Between has two arcsTwo people split everyone else into two arcs holding $n - 2$ people in all. 'Counted from the left of X' walks one way only.
7. 7Read neighbour clues'Next to both A and B' puts that person in the seat between them. Someone who may sit beside only two of the others has those two as neighbours.
8. 8Same answer, every caseTwo seatings may survive every clue. Before choosing 'cannot be determined', check whether the asked seat is the same in both.
9. 9Two details per seatWhen each person also has a sport or a job, seat the detail with the tightest clue first ('opposite Gauri'), then let the names fill in around it.