



 
Brian, Sorry that this answer is probably too late to be useful. The perfect schedule does not exist. I have a program that checks all possible schedules and selects one that is “most balanced” in terms of the number of times the players are paired together. The computation took about 2 weeks, and involved checking a total of 7945737452 schedules Here’s the most balanced schedule it found. The 15 positions in each sequence are the 15 players, and the numbers indicate the different fivesomes.
Maybe this will be useful to someone in the future.  


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