Math CentralQuandaries & Queries


Question from Jane:

My weekly golf league has 12 players in 4 threesomes.
How many weeks would it take to play everyone once and not have too many
duplications? What would be the schedule each week?


Each person plays with at most 2 "new" people each week. There are 11 people to play with, so at least 6 weeks are required. I don't know if 6 weeks is achievable.

Honestly, I don't know how to construct the schedule offhand, but here is a suggestion. Start with the 5 week schedule for 16 players playing in four foursomes. You can find it in the archives. Delete players 13, 14, 15 and 16 from the schedule. This will give four weeks of four threesomes and one week of three foursomes. In this schedule every two players are together exactly once.

If you don't like the week with three foursomes, then break it up. The pairs of players who don't play together in one of the other weeks are exactly the ones in each foursome. Unfortunately, it will take 4 more weeks to cover those pairs, and there will be some pairs of players who play together two or three times.

A different suggestion is to use the four weeks of four threesomes several times over but change which player corresponds to which number. This way, players that didn't together in the first 4 weeks will probably play together in the next 4 weeks, and so on.

Neither solution is perfect, I'm afraid.


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