Barbara,

It seems that you can’t. I have a program that checks all of the possible schedules, so long as the number of possibilities is small enough to check by computer in less than a couple of days.

The most balanced schedule for two threesomes over 5 days (according to equalizing the number of times each pair is together) is pasted below.

Day 1 : (0, 0, 1, 0, 1, 1)
Day 2 : (0, 1, 0, 1, 0, 1)
Day 3 : (0, 1, 1, 0, 0, 1)
Day 4 : (0, 0, 1, 1, 0, 1)
Day 5 : (0, 0, 0, 1, 1, 1)

The 6 players are the 6 positions in the lists The numbers indicate the groups on the day. For example, on Day 1 the threesomes are 1, 2, 4 and 3, 5, 6. This schedule is less than perfect: players 1 and 6 are never together, whereas 1 and 2 are together three times.

—Victoria