title: Arrange 14 people into groups of 4 such that every person meets once minimum
body: <p>I have 14 people in a room, and a table with 4 chairs in the middle of the room. I want each person to sit at the table with every other person at least once (i.e. they meet every other person in the room by sitting at the table with them, in groups of 4). I'm wondering what the minimum number of groups I need is and how I can find these groups algorithmically.</p>
  <p>Weirdly enough this isn't a homework problem, but a family member is trying to organize a zoom call, and as a maths student it has interested me. I've looked around and found this article trying something similar (<a href="http://zulko.github.io/blog/2013/11/08/placing-your-employees-so-that-everyone-meets/" rel="nofollow noreferrer">http://zulko.github.io/blog/2013/11/08/placing-your-employees-so-that-everyone-meets/</a>) and considered the social golfer problem (<a href="https://www.metalevel.at/sgp/#:%7E:text=The%20Social%20Golfer%20Problem%20(SGP,denoted%20by%20the%20triple%20g%2Dp%2Dw.)" rel="nofollow noreferrer">https://www.metalevel.at/sgp/#:~:text=The%20Social%20Golfer%20Problem%20(SGP,denoted%20by%20the%20triple%20g%2Dp%2Dw.)</a> but I'm still unsure. I got 23~ with some really disorganized paper scribblings which I now can't decipher.</p>