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| Math Central | Quandaries & Queries |
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Question from Brian: I am trying to arrange 5 rounds of golf for 15 golfers. We will play 5 in a group, 3 groups per round, 5 rounds. I would like everyone to play with everyone else. Secondary objective would be for no one to play with anyone else more than 2 times. Thank you. |
Brian,
Sorry that this answer is probably too late to be useful. The perfect schedule does not exist. I have a program that checks all possible schedules and selects one that is “most balanced” in terms of the number of times the players are paired together. The computation took about 2 weeks, and involved checking a total of 7945737452 schedules
Here’s the most balanced schedule it found. The 15 positions in each sequence are the 15 players, and the numbers indicate the different fivesomes.
Day 0 : (0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2)
Day 1 : (0, 0, 1, 1, 2, 0, 0, 1, 2, 2, 0, 1, 1, 2, 2)
Day 2 : (0, 1, 0, 1, 2, 0, 1, 2, 0, 2, 2, 1, 2, 0, 1)
Maybe this will be useful to someone in the future.
—Victoria
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