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Someone asked about holding a series of meeting with subgroups of people and wanted to insure during any round of the meetings that people would meet at a different location than the previous round and with a different mix of people. So on the first round of meetings, Allen, Barb, Charlie, and Denise would meet at location E and Fred, Gina, Harry, and Iona would meet at location J. On the next round, you'd mix things up so that it wasn't the same four people at the same location. There's a lot of information in Statistics on how to do something like this, and a good starting point would be a latin square design.
There's a simpler rule that I learned when I was part of a bridge group. At each table, the four players would be assigned numbers 1 through 4. After the first round, the first player would advance one table, the second player would advance two tables, and so forth. Here's a simple Excel spreadsheet that illustrates how this would work for six tables.
If you're really adventurous, you can look at the branch of mathematics called group theory.