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Requests / Re: Request: 24 players 4v4; 10 games
« Last post by Ian Wakeling on May 20, 2024, 12:41:22 PM »My thinking is that there are no good solutions for the length of tournament that you are looking for, in particular the opposition part of your 5th bullet point is the problem. The 8 round solutions that I have managed to make are really bad, so instead I am offering a 7 round solution.
(1 10 20 22 v 4 5 7 11) (6 9 16 23 v 8 12 13 17) (2 14 15 24 v 3 18 19 21)
(2 11 21 22 v 5 6 1 12) (7 10 17 23 v 9 13 14 18) (3 8 16 24 v 4 19 20 15)
(3 12 15 22 v 6 7 2 13) (1 11 18 23 v 10 14 8 19) (4 9 17 24 v 5 20 21 16)
(4 13 16 22 v 7 1 3 14) (2 12 19 23 v 11 8 9 20) (5 10 18 24 v 6 21 15 17)
(5 14 17 22 v 1 2 4 8) (3 13 20 23 v 12 9 10 21) (6 11 19 24 v 7 15 16 18)
(6 8 18 22 v 2 3 5 9) (4 14 21 23 v 13 10 11 15) (7 12 20 24 v 1 16 17 19)
(7 9 19 22 v 3 4 6 10) (5 8 15 23 v 14 11 12 16) (1 13 21 24 v 2 17 18 20)
The pairs of players within a team of 4 are the best they can be - so everyone is partnered with 21 different players. As mentioned above, the balance for opponents is not so great - players 1 to 21 have 5 other players who they never oppose and one other player who they oppose 3 times; players 22 to 24 all have 9 other players who they never oppose, and 7 other players who they oppose 3 times, so the last three players get a raw deal.
It's worth mentioning that if you were to have a 23 round schedule, then I think full balance would be possible with each player having every other player 3 times as a partner, and 4 times as an opponent.
(1 10 20 22 v 4 5 7 11) (6 9 16 23 v 8 12 13 17) (2 14 15 24 v 3 18 19 21)
(2 11 21 22 v 5 6 1 12) (7 10 17 23 v 9 13 14 18) (3 8 16 24 v 4 19 20 15)
(3 12 15 22 v 6 7 2 13) (1 11 18 23 v 10 14 8 19) (4 9 17 24 v 5 20 21 16)
(4 13 16 22 v 7 1 3 14) (2 12 19 23 v 11 8 9 20) (5 10 18 24 v 6 21 15 17)
(5 14 17 22 v 1 2 4 8) (3 13 20 23 v 12 9 10 21) (6 11 19 24 v 7 15 16 18)
(6 8 18 22 v 2 3 5 9) (4 14 21 23 v 13 10 11 15) (7 12 20 24 v 1 16 17 19)
(7 9 19 22 v 3 4 6 10) (5 8 15 23 v 14 11 12 16) (1 13 21 24 v 2 17 18 20)
The pairs of players within a team of 4 are the best they can be - so everyone is partnered with 21 different players. As mentioned above, the balance for opponents is not so great - players 1 to 21 have 5 other players who they never oppose and one other player who they oppose 3 times; players 22 to 24 all have 9 other players who they never oppose, and 7 other players who they oppose 3 times, so the last three players get a raw deal.
It's worth mentioning that if you were to have a 23 round schedule, then I think full balance would be possible with each player having every other player 3 times as a partner, and 4 times as an opponent.