12 team 1v1v1

[Tracorre]

I am trying to create a tournament for 12 teams playing in 1v1v1 matches.  I figured over 11 weeks(4 1v1v1 each week) I should be able to get each team to have played each other team twice but for the life of me I can't get it to work.  Anyone with any idea about 1v1v1 scheduling that could help?

[Ian Wakeling]

It is  possible to have all the teams face each other exactly twice.  For example the following schedule:

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

The whole thing can be generated from the first round,  team 12 remains fixed, while the other teams cycle around 1 to 11.

Hope that helps.

[Tracorre]

Indeed it does, I had tried similar but not gotten it to work.  How do you figure the correct first round to use?

[Ian Wakeling]

Have a look at this thread in particular reply #7.  In your case team 12 represents infinity and the other teams are the residues mod 11.  You should be able to verify that all 5  non-zero differences mod 11 occur twice.