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Not sure if this is the right place to ask this, but here goes (fingers crossed that someone can point me in the right direction):

I am planning a singles "speed dating" type event, but it's a little bit complicated.

Here's the requirements:

12 men and 12 women will be seated in groups of 4 (2 men and 2 women) for short periods of time. They will then each switch to a different group at a different table ("Table Change") with the goal being that every man gets to meet with every woman at least once and vice versa. The goal is to minimize duplication at the tables after each table change. How many separate tables do I need to achieve the goal within 6 table changes? I thought 36 different groupings would get me to where I need to be but now I think that's wrong.

To clarify (based on comments below), the goal here is to avoid the 2 men staying together each time or the 2 women staying together each time. Instead, the goal is to have the men and women at each table, upon each "table change" be 4 different people...at least, as much as possible. The goal is 6 tables of 4 that are completely different each time such that each time there is a table change, everyone at the table is new to everyone else. I don't know if that is possible with 6 tables & 6 table changes. If it is not mathematically possible, then we can have people "repeat" at a table with someone they met at a prior table, but then the question becomes, what is the minimum number of tables & table changes needed so that all 12 men meet all 12 women, and all 12 women meet all 12 men, with as few repeats and as much variation among the 4 people at each table?

Thanks in advance for any thoughts!

Signed,

Not a math wiz like so many of you on this site.

Desperate
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  • In a group of four, do the two men get to meet both women in their group or only one of the two women in the group? –  Jan 04 '14 at 10:23
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    A simple approach would be to take six tables, seat two women at each table and let the men rotate (politely, they late the ladies keep their seats) from table to table in six roounds. For every man and every woman there is exactly one round where they meet aat a table. But the men always "compete" against the same man, likewise for the women - but any need to avoid that was not part of the problem statement. – Hagen von Eitzen Jan 04 '14 at 11:40
  • Thanks for your question! Yes, in each group, both men will talk to both women at the table. Upon each table change, all 4 people must move to a new table so that all 4 people are sitting w/new people. I've given up on trying to do this in a way in which no one repeats w/another person (feels impossible w/tables of 4 but I might be wrong about that). It's more important for each man to eventually talk to each woman & for each woman to eventually talk to each of the men & to try to mix each table up upon each table change. Thoughts? Thank you so much again for the question!! – Desperate Jan 04 '14 at 15:51

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