I have 40 people and 10 tables that can accommodate 4 people at a time. The task is to make sure that every person seats with every other person at the same table exactly once, that is every person needs to be at the same table with with the other 39, so the whole thing will take 13 iterations. So, if in the first iteration person A sat with people B, C, and D they should never seat at the same table again. The nature of a event is like a speed dating but for business networking, so meet-ups are done in parallel. Please advise

  • $\begingroup$ The structure you describe is a pairwise balanced uniform design, or BIBD, with parameters $v=40, b=130, r=13, k=4, \lambda=1$. I'm not sure if one exists, but this can help you focus your research. It's resolvable with 13 parallel classes. $\endgroup$ Jul 22, 2023 at 11:51
  • $\begingroup$ According to this paper, I believe you can construct a solution using $\text{PG}(3, 3):1$ $\endgroup$ Jul 22, 2023 at 15:51
  • $\begingroup$ What is the question? $\endgroup$
    – Neal Young
    Jul 23, 2023 at 21:29


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