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I am a musician who plays in Celtic sessions. Typically 5 to 20 of us crowd into a pub or living room, but due to Covid-19 physical distancing recommendations, we now have to play outside in a big field.

What seating arrangement provides maximum closeness to each other while still maintaining the minimum distance from each other at all times? Also, since people arrive at different times, and the total number varies depending on who comes, in which order should the seats be occupied?

Constraints:

  • 2-metre separation from every other person (Canada)
  • need a way to get from your seat to the bathroom without getting closer than 2m to anyone
  • we need to hear each other

In a big field, people at the edges can walk away, so no bathroom problem.

For a circle, note that it's hard to hear someone on the far side. A hexagonal system traps the person at the centre of the hexagon.

The following arrangement is my suggestion. The numbers represent seating order and a dot represents a chair. Note that "inner" people can exit via the aisle, while those in the outer chairs can simply walk away:

Covid-19 seating suggestion

Comments? Thanks.

Eric O
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    What are you trying to optimise? Perhaps the minimise the greatest distance between individuals? – Henry Jun 14 '20 at 19:06
  • Minimize distance between people (players) within the constraints. Everyone wants to hear everyone else. – Eric O Jun 14 '20 at 20:32
  • The greatest distance? The sum of the distances? Something else? – Henry Jun 14 '20 at 23:08
  • I don't know. Perhaps minimize the greatest distance? – Eric O Jun 15 '20 at 04:34
  • I doubt this is easy, but your diagram has a maximum distance of $8\sqrt{2} \approx 11.31$. You could reduce this to about $10.43$ if you squeezed up the top row and moved it closer the second top row. There are likely to be better possibilities – Henry Jun 15 '20 at 09:27
  • I see what you mean about squeezing top (and bottom) rows, since those people can get to bathroom outwards. But the idea is meant to be scalable. What if 30 people show up? – Eric O Jun 15 '20 at 17:43

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