Hi Christie,
I think the following schedule will work well for 28 players. Each player should have 13 different partners and 26 different opponents (all but one of the 27 possible opponents exactly once). Clearly there must be some overlap, so each player will have 12 or 13 other players with whom they play both as partners and opponents.
( 5 1 v 10 4) (23 13 v 2 7) (21 19 v 9 6) (20 25 v 3 24) (12 18 v 26 27) ( 8 17 v 14 15) (28 22 v 11 16)
( 6 2 v 11 5) (24 1 v 3 8) (22 20 v 10 7) (21 26 v 4 25) (13 19 v 14 27) ( 9 18 v 15 16) (28 23 v 12 17)
( 7 3 v 12 6) (25 2 v 4 9) (23 21 v 11 8) (22 14 v 5 26) ( 1 20 v 15 27) (10 19 v 16 17) (28 24 v 13 18)
( 8 4 v 13 7) (26 3 v 5 10) (24 22 v 12 9) (23 15 v 6 14) ( 2 21 v 16 27) (11 20 v 17 18) (28 25 v 1 19)
( 9 5 v 1 8) (14 4 v 6 11) (25 23 v 13 10) (24 16 v 7 15) ( 3 22 v 17 27) (12 21 v 18 19) (28 26 v 2 20)
(10 6 v 2 9) (15 5 v 7 12) (26 24 v 1 11) (25 17 v 8 16) ( 4 23 v 18 27) (13 22 v 19 20) (28 14 v 3 21)
(11 7 v 3 10) (16 6 v 8 13) (14 25 v 2 12) (26 18 v 9 17) ( 5 24 v 19 27) ( 1 23 v 20 21) (28 15 v 4 22)
(12 8 v 4 11) (17 7 v 9 1) (15 26 v 3 13) (14 19 v 10 18) ( 6 25 v 20 27) ( 2 24 v 21 22) (28 16 v 5 23)
(13 9 v 5 12) (18 8 v 10 2) (16 14 v 4 1) (15 20 v 11 19) ( 7 26 v 21 27) ( 3 25 v 22 23) (28 17 v 6 24)
( 1 10 v 6 13) (19 9 v 11 3) (17 15 v 5 2) (16 21 v 12 20) ( 8 14 v 22 27) ( 4 26 v 23 24) (28 18 v 7 25)
( 2 11 v 7 1) (20 10 v 12 4) (18 16 v 6 3) (17 22 v 13 21) ( 9 15 v 23 27) ( 5 14 v 24 25) (28 19 v 8 26)
( 3 12 v 8 2) (21 11 v 13 5) (19 17 v 7 4) (18 23 v 1 22) (10 16 v 24 27) ( 6 15 v 25 26) (28 20 v 9 14)
( 4 13 v 9 3) (22 12 v 1 6) (20 18 v 8 5) (19 24 v 2 23) (11 17 v 25 27) ( 7 16 v 26 14) (28 21 v 10 15)
32 players and 13 weeks is a much harder problem to solve. Is there any flexibility in the number of weeks, as I think I could find a better schedule for 15 weeks rather than 13 weeks?
Ian.
Hi Christie,
Here is the equivalent 32 player schedule in 15 rounds, it has properties that are similar to the 28 player version above.
(30 21 v 22 26) (10 19 v 25 17) ( 1 3 v 24 11) ( 6 28 v 16 31) ( 2 32 v 8 20) (29 9 v 5 12) (14 15 v 13 27) ( 7 4 v 18 23)
(16 22 v 23 27) (11 20 v 26 18) ( 2 4 v 25 12) ( 7 29 v 17 31) ( 3 32 v 9 21) (30 10 v 6 13) (15 1 v 14 28) ( 8 5 v 19 24)
(17 23 v 24 28) (12 21 v 27 19) ( 3 5 v 26 13) ( 8 30 v 18 31) ( 4 32 v 10 22) (16 11 v 7 14) ( 1 2 v 15 29) ( 9 6 v 20 25)
(18 24 v 25 29) (13 22 v 28 20) ( 4 6 v 27 14) ( 9 16 v 19 31) ( 5 32 v 11 23) (17 12 v 8 15) ( 2 3 v 1 30) (10 7 v 21 26)
(19 25 v 26 30) (14 23 v 29 21) ( 5 7 v 28 15) (10 17 v 20 31) ( 6 32 v 12 24) (18 13 v 9 1) ( 3 4 v 2 16) (11 8 v 22 27)
(20 26 v 27 16) (15 24 v 30 22) ( 6 8 v 29 1) (11 18 v 21 31) ( 7 32 v 13 25) (19 14 v 10 2) ( 4 5 v 3 17) (12 9 v 23 28)
(21 27 v 28 17) ( 1 25 v 16 23) ( 7 9 v 30 2) (12 19 v 22 31) ( 8 32 v 14 26) (20 15 v 11 3) ( 5 6 v 4 18) (13 10 v 24 29)
(22 28 v 29 18) ( 2 26 v 17 24) ( 8 10 v 16 3) (13 20 v 23 31) ( 9 32 v 15 27) (21 1 v 12 4) ( 6 7 v 5 19) (14 11 v 25 30)
(23 29 v 30 19) ( 3 27 v 18 25) ( 9 11 v 17 4) (14 21 v 24 31) (10 32 v 1 28) (22 2 v 13 5) ( 7 8 v 6 20) (15 12 v 26 16)
(24 30 v 16 20) ( 4 28 v 19 26) (10 12 v 18 5) (15 22 v 25 31) (11 32 v 2 29) (23 3 v 14 6) ( 8 9 v 7 21) ( 1 13 v 27 17)
(25 16 v 17 21) ( 5 29 v 20 27) (11 13 v 19 6) ( 1 23 v 26 31) (12 32 v 3 30) (24 4 v 15 7) ( 9 10 v 8 22) ( 2 14 v 28 18)
(26 17 v 18 22) ( 6 30 v 21 28) (12 14 v 20 7) ( 2 24 v 27 31) (13 32 v 4 16) (25 5 v 1 8) (10 11 v 9 23) ( 3 15 v 29 19)
(27 18 v 19 23) ( 7 16 v 22 29) (13 15 v 21 8) ( 3 25 v 28 31) (14 32 v 5 17) (26 6 v 2 9) (11 12 v 10 24) ( 4 1 v 30 20)
(28 19 v 20 24) ( 8 17 v 23 30) (14 1 v 22 9) ( 4 26 v 29 31) (15 32 v 6 18) (27 7 v 3 10) (12 13 v 11 25) ( 5 2 v 16 21)
(29 20 v 21 25) ( 9 18 v 24 16) (15 2 v 23 10) ( 5 27 v 30 31) ( 1 32 v 7 19) (28 8 v 4 11) (13 14 v 12 26) ( 6 3 v 17 22)
What you say is essentially correct, things will still be good if you start removing rounds from the 15 round schedule. However the program I used to find the schedule also tries to balance the total number of times that players play together in the same match, regardless of whether they are partners or opponents. This social balance will be slightly upset by removing some rounds above, so it might be possible to do a little better.
Ian.