Queer math

[the_fantastic_ms_fox]

I just sent this email off to a queer speed-friending/dating site.

.......................................

I would love to know how you solved the combinatoric/organizing problem inherent in queer speed friending/dating. I've filled many a piece of paper trying (and failing) to figure it out and present it in a simple form so that participants could follow instructions.

Hetero speed dating is fairly simple - everyone in group A (i.e. women who like guys) has to meet everyone in B (i.e. guys who like women), but neither A nor B is to meet anyone in their own group - you just form an inner and outer circle and one rotates. There are n people; n/2 in A and n/2 in B and you have n^2/4 meetings with n/2 happening at per turn with n/2 turns.

Same-sex speed dating is a more complicated as it requires n*(n-1)/2 meetings and the double-circle method fails to introduce everyone to everyone else. How did you do it so that everyone meets each-other without making the instructions too complicated for participants to follow? Did you group everyone into groups A and B, do the double-circle for one complete rotation then subdivide A and B and repeat with two double circles, repeating until done?

I could see it work if you had 4, 8, 16, 32 and so on people and could give everyone a slip of paper with who they need to talk to next, or a number slightly below an exponent of two, with a few people sitting out each round

I'd love to know how you did it - and I'd like to attend the next 19+ Rhizome event too,

- Amy

Comments

[osmie]

This is exactly the same problem as constructing a round-robin tournament in any field of competition -- which, interestingly, is also isomorphic to sudoku, but that's another digression.

Typically what happens¹ is that all the tables are numbered from 1 to N, with one side of each table designated, "Move up a table," and the other designated, "Move down a table." Two chairs are special. Instead of a "Move up" chair, table #N has one which says, "Switch to the other side of this table; you'll be moving down from table to table henceforth." And instead of a "Move down" chair, table #1 has one which says, "Stay where you are."

Whoever's in the "up" chair of table #2 is dating the person two spots behind them. Whoever's in the "up" chair of table #3 is dating the person four spots behind them. Whoever's in the "up" chair of table #(N/2) is dating the person (N-2) spots behind them, which also happens to be the person one spot in front of them. Meanwhile, whoever's in the "up" chair of table #1 is dating the person in the "stay here" chair.

After (N-1) rounds, the (N-1) people playing musical chairs will each sit everywhere once, and as long as everyone follows instructions, you'll end up matching every possible pair of people.

¹OK, these days what typically happens is that the tournament organizers use a software package like tsh or tourneyman which spits out any arbitrarily complex pairing scheme, and even accommodates players who accidentally played the wrong opponent dated the wrong candidate last round. What I'm describing is the low-tech solution.

[osmie]

Sorry, I mean the tables are numbered from 1 to (N/2). It wouldn't make much sense to have as many tables as you have participants.

[darthmaus.livejournal.com]

You are both nerd-tastic.