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.
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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 opponentdated the wrong candidate last round. What I'm describing is the low-tech solution.