A longtime friend of the family emailed me the other day with a problem. She is organizing an event intended to help a group of people network with one another. The people are divided into groups of equal size, and each group sits at their own table together. Members of each group get some time to meet one another, and then they move on to a different table with a new group of people. In addition, one of the six people at each table is a facilitator who does not rotate. The question is: is there a way to assign people to tables for each rotation such that they meet as many new people as possible? In my friend's case, there are six tables with six seats each, and there are 36 attendees (including the six facilitators).
It's kind of an interesting combinatorics problem, or maybe it's only interesting because I last took a class involving combinatorics roughly 15 years ago. I'll describe my solution after the jump, comments are welcome on its validity.
