Here's an interesting problem that I came up with the other night.
With straight speed dating, (assuming the number of men and women are equal) the number of iterations that need to be made before every man has chatted with every woman is N/2, where N is the total number of people.
Gay speed dating is much more complex. The traditional model obviously won't work. Assuming in straight speed dating, the men stay at their tables, the "sitting" men in gay speed dating won't meet one another (nor will the "standing" men).
Counting combinations in gay speed dating manually, I see the following numbers:
f(2) = 1 f(3) = 3 f(4) = 3 f(5) = 5 f(6) = 5
These numbers suggest that gay speed dating can be done with N or N-1 iterations (albeit in a much more chaotic pattern).
Anyone have any ideas? Also, if it is N iterations, would there be a pattern that could be followed? I.e.: could the gentlemen circle a rectangular table in a clockwise fashion, then rearrange themselves and continue in another fashion such that given any number of men, every man would be paired with every other man in the smallest number of iterations and without pairing two men together twice.