<p>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</p>

CC BY-SA 4.0
2023-07-22T11:51:22.757Z
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.
Command Master
CC BY-SA 4.0
2023-07-22T15:51:42.530Z
According to [this](http://library.isical.ac.in:8080/jspui/bitstream/10263/669/1/61.51.pdf) paper, I believe you can construct a solution using $\text{PG}(3, 3):1$
Command Master
CC BY-SA 4.0
2023-07-23T21:29:11.630Z
What is the question?
Neal Young
<ds.algorithms><ds.data-structures><pr.probability><permutations>
Speed networking algorithm
Helen Grey
# Speed networking algorithm

(Asked by: username_0 on 2023-07-21)

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

**Tags:** ds.algorithms, ds.data-structures, pr.probability, permutations
> **Comments:**
> **username_1**: 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.  
> **username_1**: According to [this](http://library.isical.ac.in:8080/jspui/bitstream/10263/669/1/61.51.pdf) paper, I believe you can construct a solution using $\text{PG}(3, 3):1$  
> **username_2**: What is the question?  

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## 0 answers

