Math CentralQuandaries & Queries


Question from Scott:

I need to schedule 9 teams on 3 fields for 18 days with no buys. Two teams play while other practices in field(little guys). Two fields have backstops and other is open field. Would like to have even time on each diamond if possible. Thank you


Here’s a suggestions that works almost as you want. I don’t know if it is possible to tweak the field scheduling to make it perfect.

The following schedule has every 3 teams together exactly once over 4 days.

Day 1: 1, 4, 7; 2, 5, 8; 3, 6, 9
Day 2: 1, 5, 9; 2, 6, 7; 3, 4, 8
Day 3: 1, 6, 8; 2, 4, 9; 3, 5, 7
Day 4: 1, 2, 3; 4, 5, 6; 7, 8, 9

If you use it three times, then every two teams will have played exactly once. For example with the triple 1, 4, 7, then the first time 1 plays 4, the second time 1 plays 7 and the 3rd time 4 plays 7.

For the remaining 6 days you can use it 1.5 more times. The schedule isn't perfectly balanced in terms of the number of times each two teams play.

To schedule the fields,

  • the first time through use fields A, B, C on Day 1; B, C, A on Day 2; C, A, B on Day 3, and A, B, C on Day 4.

  • the second time through use B, C, A on Day 1, and rotate as above.

  • the third time through use C, A, B on Day 1, and rotate as above.
At this point each team has been on each field four times.

For the remaining 6 days you can schedule the fields similarly, but the number of times on each field might not end up being perfectly balanced.

Good luck!

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