Annual bocce tournament, 12 teams, 8 weeks

[Chris99]

Each team plays one team per week, and each team ends up not playing 3 teams during the tournament. I want the top 3 / bottom 3 teams not to play each other; roughly the same teams play every year, so top 3 / bottom 3 are based on last year's results. I've tried juggling combos but haven't figured it out. Any help appreciated.

Thanks,
Chris

[Ian Wakeling]

Chris,

There are 9 matches that you want to exclude and it is possible to achieve this.  If the best three teams are 1 to 3, and the bottom three are 11 to 12, then in the following (column balanced) round robin, all 9 of these matches occur in the top left hand 3x3 sub-square - so you need to use rounds 4 to 11 for your schedule. An inevitable consequence of doing this is that 9 matches between relatively closely matched teams (see the top right hand sub-square are also excluded).

Hope that helps,

Ian.

( 1 12) ( 2 11) ( 3 10) ( 6  7) ( 8  9) ( 4  5)
( 3 11) ( 1 10) ( 2 12) ( 5  8) ( 4  6) ( 7  9)
( 2 10) ( 3 12) ( 1 11) ( 4  9) ( 6  8) ( 5  7)
( 4 10) ( 7 12) ( 5  9) ( 8 11) ( 1  3) ( 2  6)
( 4  7) ( 3  5) ( 2  8) ( 6 12) ( 1  9) (10 11)
( 3  8) ( 2  9) ( 6 10) ( 1  7) ( 5 12) ( 4 11)
( 1  6) ( 4  8) ( 7 11) ( 2  3) ( 5 10) ( 9 12)
( 8 12) ( 9 10) ( 1  4) ( 5 11) ( 2  7) ( 3  6)
( 9 11) ( 7  8) ( 5  6) (10 12) ( 3  4) ( 1  2)
( 2  5) ( 6 11) ( 4 12) ( 3  9) ( 7 10) ( 1  8)
( 6  9) ( 1  5) ( 3  7) ( 2  4) (11 12) ( 8 10)

[Chris99]

Ian,

     Great, thanks! Just curious, from a programming standpoint, how did you get the 3x3 subset?

Thanks,
Chris

[Ian Wakeling]

Chris,

Essentially I have fixed the 9 matches in the positions shown above, and then moved the other 57 matches around until a balanced schedule is found.  The criteria for balance being: each team once per row, and each team once or twice per column.  Does that help?

Ian.

[Chris99]

Ian,

    Yes, it does. Thanks!

Chris