classroom combinatorics

*To*: mathgroup at smc.vnet.net*Subject*: [mg111428] classroom combinatorics*From*: "McGill, Paul" <mcgill at mbari.org>*Date*: Sun, 1 Aug 2010 04:56:04 -0400 (EDT)

My wife, who is a business professor, asked me an interesting question today. She has 28 students in her class and wants them to meet in groups four, once each class session, such that every student gets at least one chance to work with every other student in a minimum number of class sessions. For instance, if the class had only nine students and met in groups of three, you could accomplish this in four class sessions: c1 = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}} c2 = {{1, 4, 7}, {2, 5, 8}, {3, 6, 9}} c3 = {{1, 5, 9}, {2, 6, 7}, {3, 4, 8}} c4 = {{1, 6, 8}, {2, 4, 9}, {3, 5, 7}} How can I use Mathematica to figure this out? I've looked through the tutorial for the Combinitorica package and see nothing quite like this case. Can anyone give me a nudge in the right direction? Thanks, Paul