Seating Arrangement
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How seating puzzles are set
Circular neighbour rule
L(i) = (i+1) \bmod n,\quad R(i) = (i-1) \bmod n
Seats numbered clockwise, everyone facing the centre. Both swap if facing outward.
Opposite seat
i \leftrightarrow (i + n/2) \bmod n
Only when n is even. An odd table has no opposite seat.
People between two seats
\text{between} = |a - b| - 1
a and b are seat numbers in the same row.
Viewer versus person
\text{person faces south} \Rightarrow \text{their left} = \text{your right}
Applies to the person's own left and right, never to the row ends.