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| Math Central | Quandaries & Queries |
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Question from Bill: I have a group of 12 golfers playing 6 rounds of golf. I am looking for a pairings schedule that allows each golfer to play at least one round in a foursome with each of the other eleven players. Can you provide me with a solution? |
Bill,
Unfortunately a best possible schedule involves too much checking for my computer to find in less than a month. Here is a pretty good one. It was the best of the random sample of several million schedules that were generated, and it beat the one produced by the approximation method that usually does very well. I hope it does what you want. It is the best I can do.
Day 0 : (0, 0, 0, 1, 1, 2, 1, 2, 2, 0, 2, 1)
Day 1 : (0, 1, 2, 0, 1, 1, 0, 0, 1, 2, 2, 2)
Day 2 : (0, 1, 2, 1, 0, 2, 2, 0, 2, 0, 1, 1)
Day 3 : (0, 1, 2, 0, 2, 0, 1, 1, 2, 1, 0, 2)
Day 4 : (0, 1, 2, 2, 2, 1, 0, 1, 0, 2, 0, 1)
Day 5 : (0, 1, 2, 2, 1, 2, 2, 1, 0, 0, 1, 0)
On each day, the players correspond to the 12 positions in the list and the numbers indicate the foursomes. On day 0 (the first day), the groups are 1, 2, 3, 10; 3, 4, 6, 12; 5, 7, 8, 11.
The order of the days and the numbering of the groups on each day can be changed without affecting anything.
--Victoria
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