Math CentralQuandaries & Queries


Question from Andy:

I am having difficulty scheduling pairings for a forthcoming Golf holiday. There are 7 players and we will be playing 7 rounds - each round will be a 3 ball and a 4 ball. I am trying to work out a schedule that means everyone plays with each other roughly the same number of times (with a minimum of, say, 3 times if possible). Also, we are looking to ensure everyone plays in roughly the same number of 3 and 4 balls. Any suggestions would be much appreciated (we leave in 10 days time). Thank you.


There is a schedule of seven threesomes that has each pair playing together exactly once:

1, 3, 7; 2, 4, 1; 3, 5, 2; 4, 6, 3; 5, 7, 4; 6, 1, 5; 7, 2, 6.

The remaining four players form the foursome each time. At the end of seven rounds each pair of players will have played together exactly three times. Each player is in three 3-balls and four 4-balls.

Hope this helps.

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