SEARCH HOME
 Math Central Quandaries & Queries
 Question from Judi: How would I develop a playing schedule using foursomes and one twosome for 14 players who will play 12 weeks and each person would play all but one of the others?

Judi,

You can’t get exactly what you want. Some pairs of players will need to be together three times, I think.

There is a schedule for 16 players where every pair is together exactly once over 5 rounds. You can find it by searching for “golf 16” in the archives.

If you delete players 15 and 16 wherever they occur, then you have a schedule for 5 rounds where every pair is together once. For one of the rounds you have 3 foursomes and a twosome, and for the other 4 you have 2 foursomes and 2 threesomes.

For the first 10 weeks, use that schedule twice. The first time through it, add a player from the second threesome to the first threesome to get 3 fours and a two. The second time through, add a player from the first threesome to the second one. This schedule is pretty good. Most pairs are together twice, a few are together once. Schedule the last 2 weeks however you want; re-using week 1 and week 7 from the schedule for the first 10 weeks is not a terrible thing to do.

—Victoria

Judi wrote back

I'm still having lots of trouble scheduling my 14 players to play against each of the other girls one time during our 13 weeks. I went to golf 16 and looked at Bill's 5 week schedule, deleting player 15 and 16 but I don't know what to do next. That works for 5 weeks. For example who does player #1 play against on day (or week) 6? I can't just reuse Bill's plan cause people would be playing the same people again. Help!!!!

Judi,

With that plan every pair have been in the same group once over 5 weeks. It seems like that's not what you want (sorry for the misunderstanding): instead you want each pair to play a match together. Try this. Number the players 1 to 13 and X. First form the matches

1: 1 12; 2, 11, 3 10; 4 9; 5 8; 6 7; 13 X
2: 2 13; 3, 12; 4 11; 5 10; 6 9; 7 8; 1 X
3: 3 1; 4 13; 5 12; 6 11; 7 10; 8 9; 2 X

To get each subsequent week, add 1 to all player numbers from the current week using two rules for special cases: 13 + 1 = 1 (wrap around like an odometer), and X + 1 = X. This will give you the matches you want: every pair plays exactly one match together.

Now you want to form the foursomes. I don't have a good way of doing that to balance the number of times every two players are in a group together. For each week you might just put the severn matches together in a hat and form the groups by random draw.

Hope this helps.
--Victoria

Math Central is supported by the University of Regina and the Imperial Oil Foundation.