Seating Arrangement
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How seating puzzles are set
Circular neighbour rule
L(i) = (i+1) \bmod n,\ R(i) = (i-1) \bmod n
Seats numbered clockwise, everyone facing centre. Both swap if facing outward.
Opposite seats
i \leftrightarrow (i + n/2) \bmod n
Only when n is even; odd tables have no opposite seat.
Viewer vs person
\text{person faces south} \Rightarrow \text{their left} = \text{your right}
Applies only to the person's own left/right, never to the row ends.