Foursomes for Leagues -- 14 weeks, 36 golfers

[teecee]

I see other posts about leagues with less players, but I am looking for an algorithm to pair 36 women in foursomes over 14 weeks with the least amount of duplicates possible.  If I have to repeat after so many weeks, that would be fine.  I have tried to do this randomly for years but the ladies keep complaining that they are playing with the same people over & over.

If the alogrithm could also figure out starting holes (9 hole league) so that each lady gets to start on as many different starting holes over the season...that would be great too!!!

[Ian Wakeling]

I have found the following schedule by computer search.  I believe that you are most interested in optimizing the social mix, or the number of times players meet together in a foursome, since this is the source of the complaints I have given this property priority.  In the schedule below all pairs play together at least once and at most twice, except for the pair (17 36) who never meet. In this respect this schedule is very close to being optimal. There is moderate balance for the start-off hole (H1 to H9), player 7 never starts off from hole 5, but otherwise players start from all holes at least once and at most three times.  There are only a handful of player/start-off hole combinations that are repeated three times.

I hope that makes for a better league.

    H1 H2 H3 H4 H5 H6 H7 H8 H9

R1  29 31 17 28  3 32 20 33 34
    18 16 24  9  4  2  5 35 22
    12  8 21 13 30 26 10 11 36
    15  7  6 19 14  1 25 23 27

R2  28 23 10  4 26 16  8 29 31
    32 12 30 13 19  5 33  1 21
    25  9 36 18 22 14  2 34  3
    15 20  7 35  6 17 27 24 11

R3  34 16 31  5 15 25 29 13  8
    27 32  6 11 21 18 17 28 23
     4 24 30  9 20 36 19 10 12
    26 22 33  2 14 35  7  3  1

R4   1 13  5 25 30  8 29 19 10
    22 15  2 33 31  6 14 36 18
    20  7 34 12 23  3 35  4  9
    17 26 28 16 24 32 11 21 27

R5  31 27 23 20 32 12  5 26  2
    18  6 16  8  9 10 24  3 15
    14 29 22 28 34  4 35 11 30
    33 25 13 36 17  7 21 19  1

R6  10  1 23 14 18  9 26 25  6
    35 33 29 34 20 16 28 30 11
    22 21  4 13  3 24 31 17  5
     2 19  8  7 27 15 12 32 36

R7  24  5 35 27 26 17 32 22 28
     4  8  3 16 36 12 11 20 23
     2 19 34  7 33  6 18 29 10
    25 30 15 21  9 13  1 31 14

R8  36 13  1 23 28 19  9 15 29
    33 21 27  3 24 35 30  6 26
     7 18 25  2 12 34  4  8 16
     5 32 14 17 11 31 22 10 20

R9  16 26 20 23 11 30  3 12  5
    10 36 13 18  8 29  1 27 15
    32 24 33 22 25 21  7 35 31
    19 14  2  6 34 28  9 17  4

R10  8 20 14 31  5 22 15 30 33
    21 34 36 17 29 11 27  2  3
    35  6 32 26 13  7 19 18 25
     9  4 12 10  1 28 23 16 24

R11  7 17 26 29  1 19 36 22 12
     3 15 18 32 35 24 31  8 30
    25 10 28  4  6 27 13 14 34
    23 11  5 33 16 20  2  9 21

R12 11 12 25  1 18 22 28  5 20
    27 19 31 24  4 33  6 21 32
    30  2 29 10 17 14 16 23  7
    13  3  9 36  8 15 34 26 35

R13 36 35 18 11 27 10 21  6 24
     3  1 19 15 32 33 22 14 17
    29  4  9 30 31 23 26  7 13
    16 28 12 20  5 34 25  2  8

R14  9 28 20 22 10 35 23 34 14
     1 17 16  5 29  8 32 18 13
     6 33  4  3 21 30 36 24 19
    31 27 11 12  2 26 15  7 25

[teecee]

Thank you very much -- this is going to work great!  I already setup next year and it is exactly what I needed.