Scott,

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.
  

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!
—Victoria