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| Math Central | Quandaries & Queries |
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Question from Chris: I have a golf league 20 players and 17 weeks. We don't have teams so I just want to have everyone to play with each other the about same number of time and, hopefully, randomly distributed throughout the season. We have had situations in the past where two people play together for three weeks in a row and then not anymore for the rest of the season. From other posts, I see how to schedule the first 5 weeks without repeats but I can’t figure out an algorithm to for the rest of the season. Thanks! |
Chris,
The 5 week schedule you found has the property that most people have played together once, and each person has not played with 4 others. The golfers that have not played together fall into 4 groups of 5. Players in the same group of 5 have not played together, and every other two players have.
What I suggest doing next is using the same schedule again after renumbering the players to that 4 of the foursomes on the first day (of the second time around) come from within the groups of 5, no 2 of whom have played together yet.
And then do the same again to get weeks 11 through 15.
Use weeks 16 and 17 to fill in pairs that have not been together yet, or balance the schedule a bit more. Insert those into the schedule after week 5 and 10, respectively.
—Victoria
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