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 Question from Steve: We have 9 golfers, divided into 3 teams each day. Play is over 6 days. Can you devise a schedule to ensure pairings allow for all golfers to play at least once with all participants? Also, that the pairings have one player from another team.

Steve,

Suppose the three teams are players 1, 2, 3, players 4, 5, 6, and players 7, 8, 9. There is a schedule where, over three days, any two players on different teams have played together exactly once:

Day 1: 1, 4, 7; 2, 5, 8; 3, 6, 9
Day 2: 1, 5, 9; 2, 6, 7; 3, 4, 8
Day 3: 1, 6, 8; 2, 4, 9; 3, 5, 7

It is possible to fill in the remaining days to get every pair together at least once. Necessarily some pairs will be together more than once over the 6 days. Here is something that seems pretty good:

Day 4: 1, 2, 4; 5, 6, 7; 3, 8, 9
Day 5: 1, 3, 5; 4, 6, 8; 2, 7, 9
Day 6: 2, 3, 6; 4, 5, 9; 1, 7, 8

Maybe something like this will work for you?
--Victoria

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