Social Square for 8 teams of 8 players in 8 rounds

[dbessone]

I am trying to find a rotation of 64 players that meets the following conditions;
1. There are 8 players at each level, 8 A players, 8 B players, 8 C players to level H.
2. Players at levels B through H may only play with a specific A player once.
3. There are 8 rounds
4. Is it also possible to limit the number of times a given B through H players plays with the same B through H players?

If anyone can help, please post a reply.
Thanks

[Ian Wakeling]

Below is a "Social Square" for 64 players in 9 rounds.  In any one round there are 8 rows corresponding to the 8 teams (or brackets of 8 players).  Any given pair of players occurs together in a row exactly once.

Round 1
 1  2 47 11 12 38 48 37
 3  4 45  9 10 40 46 39
 5  6 43 15 16 34 44 33
 7  8 41 13 14 36 42 35
17 18 63 27 28 54 64 53
19 20 61 25 26 56 62 55
21 22 59 31 32 50 60 49
23 24 57 29 30 52 58 51

Round 2
 1 64 42  3 62 21 23 44
 2 63 41  4 61 22 24 43
 5 60 46  7 58 17 19 48
 6 59 45  8 57 18 20 47
 9 56 34 11 54 29 31 36
10 55 33 12 53 30 32 35
13 52 38 15 50 25 27 40
14 51 37 16 49 26 28 39

Round 3
 1 45 56 32 52  5 28 41
 2 46 55 31 51  6 27 42
 3 47 54 30 50  7 26 43
 4 48 53 29 49  8 25 44
 9 37 64 24 60 13 20 33
10 38 63 23 59 14 19 34
11 39 62 22 58 15 18 35
12 40 61 21 57 16 17 36

Round 4
 1 55 50 58 16 63  8  9
 2 56 49 57 15 64  7 10
 3 53 52 60 14 61  6 11
 4 54 51 59 13 62  5 12
17 39 34 42 32 47 24 25
18 40 33 41 31 48 23 26
19 37 36 44 30 45 22 27
20 38 35 43 29 46 21 28

Round 5
 1 15 17 14  4 20 31 30
 2 16 18 13  3 19 32 29
 5 11 21 10  8 24 27 26
 6 12 22  9  7 23 28 25
33 47 49 46 36 52 63 62
34 48 50 45 35 51 64 61
37 43 53 42 40 56 59 58
38 44 54 41 39 55 60 57

Round 6
 1 61 59 29 33 27  7 39
 2 62 60 30 34 28  8 40
 3 63 57 31 35 25  5 37
 4 64 58 32 36 26  6 38
 9 53 51 21 41 19 15 47
10 54 52 22 42 20 16 48
11 55 49 23 43 17 13 45
12 56 50 24 44 18 14 46

Round 7
 1 13 46 26 22 57 34 53
 2 14 45 25 21 58 33 54
 3 15 48 28 24 59 36 55
 4 16 47 27 23 60 35 56
 5  9 42 30 18 61 38 49
 6 10 41 29 17 62 37 50
 7 11 44 32 20 63 40 51
 8 12 43 31 19 64 39 52

Round 8
 1 36 10 25 60 51 43 18
 2 35  9 26 59 52 44 17
 3 34 12 27 58 49 41 20
 4 33 11 28 57 50 42 19
 5 40 14 29 64 55 47 22
 6 39 13 30 63 56 48 21
 7 38 16 31 62 53 45 24
 8 37 15 32 61 54 46 23

Round 9
 1 54 35 40 19 49 24  6
 2 53 36 39 20 50 23  5
 3 56 33 38 17 51 22  8
 4 55 34 37 18 52 21  7
 9 62 43 48 27 57 32 14
10 61 44 47 28 58 31 13
11 64 41 46 25 59 30 16
12 63 42 45 26 60 29 15

It's not clear to me exactly what you are asking for, so please let us know if the schedule above helps.  If you used the rows of round 9 to assign players to the levels A to H, so players  1, 54, 35, 40, 19, 49, 24, &  6 would all be at level A, players 2, 53 etc.. all at level B, then all rows from rounds 1 to 8 would contain one player each from levels A to H.

Ian.