



 
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.
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  


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences. 