A golfing variation

[BTM]

I am planning a golf trip for 13 golfers in mid-June, and am struggling to ensure the best possible mix of players, trying to ensure everyone plays with everyone else at least once.
 
We are playing 4 rounds, and what makes it particularly challenging is that we have 13 golfers for Rounds 1, 2 and 3, but only 10 for Round 4. I'm looking at 3 x 3balls and a 4ball for Rounds 1, 2 & 3 and 2 x 3balls and a 4ball for Round 4. My initial attempt is as below - golfers 11, 12 &13 are not playing R4
 
R1      (2 1 4)  (3 9 10)  (11 5 6)  (8 13 7 12)
R2      (5 12 4)  (3 2 13)  (8 6 10)  (9 11 1 7)
R3      (8 4 3)  (12 2 11)  (5 1 13)  (6 10 9 7)
R4      (5 6 3)  (8 9 1)  (2 7 4 10)
 
Before I pull out what's left of my hair, I'd be most grateful for any thoughts / assistance anyone can offer.
 
Many thanks - Nick

[Ian Wakeling]

I don't think it is possible to have a balanced schedule and avoid having one player who is always in the foursome.  For example I have found the following schedule :

( 8  4  6  .) ( 7 11  3  .) (12  2 10  .) ( 5  1 13  9)
( 5  7  2  .) ( 4 13  3  .) (12  1  8  .) (10 11  9  6)
( 8  5 11  .) ( 2 13  6  .) ( 3 10  1  .) ( 9  4 12  7)
{ .  .  .  .} ( 1  6  7  .) ( 4  5 10  .) ( 2  3  8  9)

by starting with an all foursome schedule for 16 players and then cutting it back.  Player 9 is always in the foursome, the other players all have one game in a foursome. The schedule should have no pair of players who play together twice.  Hope that helps.

Ian

[BTM]

That's fantastic - many thanks Ian.

Nick