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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


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