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January 25th, 2016, 09:25 PM   #1
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From: RobShaver

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Permutation, combination or something else?

THE SETUP
I have been asked to create a "mixer" chart so that a group of people can meet each other in the following manner.

The meeting will have between one and four tables depending on the number of people attending. There will be between 5 and 16 people at this meeting.

They want at least two people at each table so, for example, if there are sixteen people there will be four tables each with four people. If there are five people then there will be two tables, one with three people and one with two people.

There will be a series of rounds where the people will sit together for a while. When a signal is given they will move to another table. We will call these sitting periods a "round". The people will be give a chart that tells them which table to sit at for each round.

We want the people to move from table to table in a fashion such that they meet as many people as possible.

QUESTIONS TO BE ANSWERED
  1. Identify what people need to be at which table for each round. (Sets of people.)
  2. How many rounds will be needed for everyone to meet everyone else once?

CONCLUSION
I've been using the letters A through P to identify the individuals and have tried to solve this for the case of sixteen people and four tables. I've tried permutations but that does not result in sets that have people meet only once.

My math is pretty rusty. Maybe this is more like dealing cards where each card can be in one hand at a time.

Any ideas on this?

Thanks.
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February 4th, 2016, 12:26 AM   #2
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Don't know if this is helpful but if we think of the simplest case, say 8 people and 4 tables, then we put 4 of them always at the same table, and the other four move around, then after four rounds everybody meet with each other.
While this is the simplest case it gives intuition for how to deal with more complex cases: at least x people should not move where x is the number of tables. The rest should each visit all other tables.
Now for the rest of the people they must go to different tables, for example if 1,2,3 started in the same table, then in the next round 2 should go to a different table than 3.
Is this a good starting point?
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