Pat,

Here is a schedule for 13 Days (or, weeks) in which every pair of teams play together exactly once. The way to read it is that the positions in each sequence are the teams, and the numbers are the games. For example, on Day 1, team 1 plays team 3, team 2 plays team 4, and so on.

Day 1 : (0, 1, 0, 1, 2, 3, 2, 3, 4, 5, 4, 6, 5, 6)
Day 2 : (0, 1, 1, 0, 2, 3, 3, 2, 4, 5, 5, 6, 6, 4)
Day 3 : (0, 1, 2, 3, 0, 1, 2, 3, 4, 5, 6, 4, 6, 5)
Day 4 : (0, 1, 2, 3, 1, 0, 3, 2, 4, 5, 6, 5, 4, 6)
Day 5 : (0, 1, 2, 3, 2, 4, 5, 6, 0, 1, 3, 4, 5, 6)
Day 6 : (0, 1, 2, 3, 3, 4, 5, 6, 1, 0, 2, 5, 6, 4)
Day 7 : (0, 1, 2, 3, 4, 2, 5, 6, 3, 4, 0, 6, 1, 5)
Day 8 : (0, 1, 2, 3, 4, 3, 5, 6, 2, 5, 6, 0, 4, 1)
Day 9 : (0, 1, 2, 3, 4, 5, 0, 6, 4, 6, 1, 2, 5, 3)
Day 10 : (0, 1, 2, 3, 4, 5, 1, 6, 6, 2, 5, 3, 0, 4)
Day 11 : (0, 1, 2, 3, 4, 5, 6, 0, 6, 5, 4, 1, 3, 2)
Day 12 : (0, 1, 2, 3, 4, 5, 6, 1, 5, 3, 6, 4, 2, 0)
Day 13 : (0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6)

To extend the schedule to 16 Days, simply choose any three of the ones listed above and use them as 14, 15 and 16. This is the most balanced schedule it is possible to have.

—Victoria