Re: classroom combinatorics

*To*: mathgroup at smc.vnet.net*Subject*: [mg111598] Re: classroom combinatorics*From*: Chris Pemberton <cjpembo at gmail.com>*Date*: Sat, 7 Aug 2010 01:30:14 -0400 (EDT)

On 08/06/2010 05:58 AM, Daniel Lichtblau wrote: > Daniel Lichtblau wrote: >> McGill, Paul wrote: >>> 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 > This is a classic example of the "social golfer problem" which has been giving mathematicians heartburn for years. From what I've read, event organizers usually resort to using pre-printed tables to do the pairings ... but it looks like someone as been kind enough to provide a Mathematica demonstration: http://demonstrations.wolfram.com/SocialGolferProblem/ This explains why you never want to go golfing with a large group of mathematicians. Chris