Math CentralQuandaries & Queries


Question from D.:

Every Sunday, 20 of us golf together in groups of 4. I am looking for a
way that each of us play with 3 other people each week and ultimately get
to play in groups that are unique. For instance if week 1, I play with 2, 3, 4
and then the next week I play with 5, 6, 7, and the 3rd week I play with 8,
9, 10 and so forth until I have played with everyone. Everybody else should be
doing the same thing. Can you give me a schedule for this and how many weeks
would it take for all of us to accomplish this where we all play with different
combinations of people. (We should not play with the same person very often or even
the same pairs of people but everyone should play with everybody else) I hope
this makes sense........whew and thanks!


Search the archive for "golf" and look for responses with 20 golfers. You'll find schedules there. The most recent one of those, answered by Chris Fisher, seems like it will work for you.

There are 190 pairs of golfers chosen from among 20 players. Each foursome accounts for 6 pairs (some of whom may have played together before), so each day accounts for 30 pairs. That means you need at least 6 weeks before everyone plays with everyone else. From what I see in the archive, I think 6 weeks will suffice too. After 6 weeks (if that's enough), renumber the players and repeat the same schedule with the same numbering.


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