The Table Plan

Eight tables, one aunt: the seating plan is a graph

Every 'cannot sit near' is a forbidden edge and every 'must sit together' is a required one. Written down that way the plan stops being taste and becomes a problem with a finite number of solutions — and usually one edge nothing satisfies.

Connected components

Groups that must stay together set the minimum table size before anything else is decided.

The unsatisfiable edge

Sometimes no arrangement works. Finding that out early is worth more than any seating software.

Round or long

Table shape changes who can talk to whom. The conversational reach of a round eight versus a long twelve.

The top table problem

One table with rules different from all the others, and the knock-on it causes in the rest of the room.

Plan in pencil

The count moves after the plan is drawn. Every time.