



 
David, It all depends on what you mean by "best". I used to program that looks through all of the possible schedules and chooses one that is "most balanced" according to some criteria. It chose this one:
The way to read the above is that the players are the positions, and the numbers indicate the threesomes. One day zero the threesomes are 1,2,3, and 4,5,6. On day five they are 1,3,4 and 2,5,6. Hope this works for you.  


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