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Ok hi all, my first question! I would like to organize a party where everyone meets everyone, the table is organized like this:

ABCD J  E IHGF 

So A can only meet B and J, and B can only meet A and C and so on. So I suppose it could be seen as a lot of groups of 3s + 1 or 2. (abc) (def) (ghi)+J , but there is also the groups (bcd) (efg) (hij)+a

How should I move them around?

I will not know exact numbers before they arrive! Any help much appreciated.

Seems a bit like this question but a bigger table! How to rotate n individuals at a dinner party so that every guest meets every other guests and How to derive a general formula for this problem? (pairs of people seated around a table)

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    also seems a bit like this: http://math.stackexchange.com/questions/58922/rearrangement-of-groups-such-that-no-two-members-meet-again?rq=12012-12-07
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    You give all of them a version of the Keirsey personality test. Then you kick out all of the introverts. They'll move themselves. More seriously, my intuition tells me that you want to do something like picking an individual say A to swap positions with the person on the opposite corner like F, while B, J, E, and G stay seated. Just a guess.2012-12-07
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    swapping with corners would be ok but BC would stay together, which seem a little ineffective!2012-12-07
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    You'd have C also swap places.2012-12-07
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    I suppose the is a finite number of possible combinations, where each member of a set of 3 is less likely to pick a set with members it's already seen, that's more dealing with it from a programming point of view than mathematical. I'd quite link to understand what I am doing?2012-12-07
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    Yes I tried on paper just moving them around and it just becomes a mess after the first move! the must be a more logical way?2012-12-07

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