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> classroom combinatorics

• To: mathgroup at smc.vnet.net
• Subject: [mg111607] > classroom combinatorics
• From: Dana DeLouis <dana01 at me.com>
• Date: Sat, 7 Aug 2010 01:32:02 -0400 (EDT)

> She has 28 students in her class and wants them to meet in groups
> four=85

You may find the following Wolfram Demonstration interesting...

http://demonstrations.wolfram.com/SocialGolferProblem

Just some other references

http://www.maa.org/editorial/mathgames/mathgames_08_14_07.html

http://mathworld.wolfram.com/KirkmansSchoolgirlProblem.html

= = = = = = = = = =
HTH  : >)
Dana DeLouis


> On Aug 1, 4:56 am, "McGill, Paul" <mcg... at mbari.org> 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