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Requests / Re: Round Robin Schedule For Changing Teams
« Last post by Ian Wakeling on August 21, 2024, 02:59:40 AM »Hi Nathan,
The 8 player scenario is a standard one where it is possible to arrange that everyone plays with each other player once, and against each other player twice. It is called a Whist schedule in combinatorial math, and you can find an example by following the "visit the pages that inspired the forum" link near the top of the page, and then following Whist tables and dialling up 8 items. You can use the same tool to get a 15 round schedule for 16 players, however I don't see that there is an easy way to cut it down to 6 rounds, instead I have a program (not Excel) that implements a search algorithm that can find a solution. I have put this below.
(15 13 v 4 14) (10 16 v 11 5) ( 6 7 v 1 12) ( 3 9 v 2 8)
( 2 12 v 5 4) ( 9 7 v 11 14) (10 15 v 1 3) ( 6 8 v 13 16)
(14 16 v 12 3) (13 11 v 2 1) ( 5 9 v 15 6) ( 8 10 v 7 4)
( 3 7 v 13 5) ( 2 14 v 10 6) ( 4 1 v 16 9) ( 8 12 v 11 15)
( 8 5 v 14 1) (16 15 v 2 7) ( 9 10 v 12 13) ( 3 6 v 4 11)
( 4 2 v 1 7) ( 8 13 v 5 12) (10 3 v 9 6) (16 11 v 14 15)
I can offer to try other combinations of players, courts and rounds.
Best regards,
Ian
The 8 player scenario is a standard one where it is possible to arrange that everyone plays with each other player once, and against each other player twice. It is called a Whist schedule in combinatorial math, and you can find an example by following the "visit the pages that inspired the forum" link near the top of the page, and then following Whist tables and dialling up 8 items. You can use the same tool to get a 15 round schedule for 16 players, however I don't see that there is an easy way to cut it down to 6 rounds, instead I have a program (not Excel) that implements a search algorithm that can find a solution. I have put this below.
(15 13 v 4 14) (10 16 v 11 5) ( 6 7 v 1 12) ( 3 9 v 2 8)
( 2 12 v 5 4) ( 9 7 v 11 14) (10 15 v 1 3) ( 6 8 v 13 16)
(14 16 v 12 3) (13 11 v 2 1) ( 5 9 v 15 6) ( 8 10 v 7 4)
( 3 7 v 13 5) ( 2 14 v 10 6) ( 4 1 v 16 9) ( 8 12 v 11 15)
( 8 5 v 14 1) (16 15 v 2 7) ( 9 10 v 12 13) ( 3 6 v 4 11)
( 4 2 v 1 7) ( 8 13 v 5 12) (10 3 v 9 6) (16 11 v 14 15)
I can offer to try other combinations of players, courts and rounds.
Best regards,
Ian