Gay speed dating
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Visit Stack Exchange Here's an interesting problem that I came up with the other night. 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).
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. Counting combinations in gay speed dating manually, I see the following numbers: These numbers suggest that gay speed dating can be done with N or N-1 iterations (albeit in a much more chaotic pattern). Also, if it is N iterations, would there be a pattern that could be followed? I run gay speed dating events and have the seating charts for 12 participants up to 22.
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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. Imagine a long table with a seat at one end and $\frac$ seats along each long side. After each round, each person moves one seat clockwise. This gets us N-1 rounds in the even case, which is optimal. It's a little complex, but essentially you split the room into 2 parts, and then have 1/2 the room meet the other 1/2.