So, decisions have been made on sessions for the BIG Event this year. Muggins here has somehow roped himself into convening an hour’s panel discussion (or somesuch) on project management, which is either going to be fun or (more likely) a bit of a nightmare. But at least I didn’t go down on my own – I took poor Ben with me. He’s been volunteered (by me, mostly) to run a meet/greet/pub trick session. The idea is a combination of a show & tell and speed dating. Or something like that.
The trouble is, there are likely to be a sizable number of people present, and we’d like everyone to meet everyone else. Precisely once. In groups.
As a result, we’ve both spent hours failing to spot the pattern. I think you can do it for a population P and group size G which satisfies P = nG(G-1), where n is the number of meetings. Then you just need to permute n sets of G identifiers (red/orange/yellow/… , triangle/square/pentagon/… , biped/quadroped/arthropod/… etc), print out those sets as cards, and hand them over to people. The rounds of meetings are thus ‘colours,’ ‘Number of sides,’ ‘number of legs,’ and so on. Job done. Unfortunately, my brain dribbled out of my ears just as I formulated this hypothesis. These days I can write, but I’m very, very rusty at this sort of stuff. Pathetic, really.
However, one of the fundamental aspects of my training as a physicist that I do recall, was to utilise tools appropriate to the circumstances. In this case: a mathematician. Conor, you’re up. I expect a neatly-argued and useful solution in the comments forthwith. Sadly, no LaTeX markup allowed.
Bonus marks to anyone who submits perl/ruby/PHP/python etc to generate the identifier patterns for me, and for alternative solutions. Particularly if they actually work, which mine probably doesn’t.
[update 3rd March: In an entirely expected development, Conor has written code in a language of which nobody else has heard. Meanwhile, a bit of gentle Googling has revealed this page, which suggests that what we’re looking at here is a form of Whist tournament. Which seems promising, until one stumbles over this page, which remarks on a failed brute force search for an 80-person solution.]