Gay speed dating

Speed Date Philadelphia™ introduces single professionals to each other at fun and exciting speed dating events and singles parties in Philadelphia.Our events take place in restaurants, lounges and other upscale venues.

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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.

You should be able to convince yourself that each person meets each other after N rounds, but you can't do better as each person needs to meet N-1 others and has to sit out once. Then you basically do the same thing for just the 1/2's all the way until everyone has met each other. Because it has attracted low-quality or spam answers that had to be removed, posting an answer now requires 10 reputation on this site (the association bonus does not count).

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