arranging a group of people into a number of tables so that everyone sits with everyone else.

A strict version is an affine plane. More generally we want a resolvable 2-design. Resolvable is the parallelism. Maybe there is something like discrete hyperbolic geometry to deal with this, but we seem to have better combinatorial ideas below.

Strict versions include Kirkman's Schoolgirl Problem (15 children walk in groups of 3, can they do this so that all pairs of girls walk together exactly once over a whole week) {oeis}

In less strict cases we allow people to meet more often, or not to meet.

The “Dagstuhl Happy Diner problem” is the version where everyone meets at least once. {oeis}

Equitable Resolvable coverings also seem to be a more strict form, where we can allow people to meet at most twice. {ref} If we have people sitting at round tables and only interacting with their neighbours, then we have the more difficult Oberwolfach Problem

part of category mathematics