This is difficult for me to solve as presented. Ideally I would like there to be only 8 rounds. Additionally I would also like to make player 17 special, in the sense that they always get to play in a threesome, then I can make a schedule with some balance.
(4 9 3 6) (8 11 10 15) (5 13 1) (2 12 14) (16 17 7)
(5 10 4 7) (1 12 11 16) (6 14 2) (3 13 15) ( 9 17 8)
(6 11 5 8) (2 13 12 9) (7 15 3) (4 14 16) (10 17 1)
(7 12 6 1) (3 14 13 10) (8 16 4) (5 15 9) (11 17 2)
(8 13 7 2) (4 15 14 11) (1 9 5) (6 16 10) (12 17 3)
(1 14 8 3) (5 16 15 12) (2 10 6) (7 9 11) (13 17 4)
(2 15 1 4) (6 9 16 13) (3 11 7) (8 10 12) (14 17 5)
(3 16 2 5) (7 10 9 14) (4 12 8) (1 11 13) (15 17 6)
Above players 1 to 16 all play in exactly 4 foursomes and 4 threesomes. Further, all pairs of players play together within the same group at least once and at most twice. It's possible to come up with a 9th round that doesn't violate this second property, but of course it will upset the balance for players 1 to 16, for example:
(1 17 8 9) (4 5 6 7) (2 10 3) (14 15 16) (11 12 13)
Hope that helps.
