Math Is Fun Forum

Paul29

Member

Registered: 2011-05-21

Posts: 4

seating charts for 3-minute meetings

Let's say I am planning a networking meeting which will be attended by 12 people.  I would like every guest to have a few minutes to sit down and talk one-on-one with every other guest.  From the combinations formula I know there are 66 possible pairings of people.  Since there are 12 people and 2 people will sit at each table, I know I'll need 6 tables.  I can also calculate that it's possible to hold all meetings with only 11 different seating arrangements.  Is there a system that will optimize each table's seating chart for the entire event?  Is this just a further application of combinations?  Thanks!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: seating charts for 3-minute meetings

Hi Paul29;

Call each person A to L

That is your 11 seating arrangements.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Paul29

Member

Registered: 2011-05-21

Posts: 4

Re: seating charts for 3-minute meetings

Thanks bobbym, that is great!  How did you do it?  I'd like to understand the theory so I could also plan for 10 people, or 16, or 20.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: seating charts for 3-minute meetings

Hi Paul29;

Like a good magician never reveals his tricks, a good mathematician must also be mystifying.

Aw what the heck, I am not a mathematician or a magician although I can make a plate of chicken disappear.

These are called Steiner Triple systems or Kirkman schoolgirl problems. They are more commonly called dinner or social golfer problems. They were first investigated by J.J. Sylvester. There is much still unknown about them and it takes a computer to solve them. Here is the page I use when I want to mystify people.

http://www.csplib.org/prob/prob010/index.html

Just remember not every number of people in groups has a solution.

Welcome to the forum!

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Paul29

Member

Registered: 2011-05-21

Posts: 4

Re: seating charts for 3-minute meetings

Thanks, I didn't realize that this type of problem was well known and even has its own name.  I looked at your link and looked at some Wikipedia entries, but they really didn't give me enough information to compute the combinations myself.

Did you compute the combinations or did you already have the solution?  I hesitate to ask a mathematician to reveal his tricks!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: seating charts for 3-minute meetings

Actually I just copied it from the page. That page contains most of them that have known solutions.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Paul29

Member

Registered: 2011-05-21

Posts: 4

Re: seating charts for 3-minute meetings

I found it, thanks.  12 golfers, pairs, 11 rounds

That's a handy site!  I'll have to study the diagrams.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: seating charts for 3-minute meetings

They will send you to other links that have more charts, or you can come back here. Good luck!

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.