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 Question from AL, a parent: I have a golf tourney where we have fourteen players and are playing five times/rounds of golf. I am trying to pair up two threesomes and two foursomes so we don't play with the same person twice or the least amount of times.

Al,

You can play with everyone exactly once if, on one of the days, you play in 3 foursomes and a twosome. It isn't possible to do it using two foursomes and two threesomes on each day: you need to "cover" 91 pairs of players, but a collection of rounds like that only covers 90 (each foursome covers 6 pairs and each threesome covers 3 pairs).

What's shown below is a schedule for 16 players to play each other exactly once over five rounds. If you delete players O and P everywhere they occur in the schedule, then you get the schedule that includes a twosome on one of the days. If you fix that up to always have two foursomes and two threesomes by adjusting the last day, then there are 3 pairs that will never play together, and two that will play together twice.

16 player schedule:

AEIM BFJN CGKO DHLP, AFKP BELO CHIN DGJM, AGLN BHKM CEJP DFIO,
AHJO BGIP CFLM DEKN, ABCD EFGH IJKL MNOP

Have fun!
Victoria

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