9 Teams, 3 Teams Per Round, 6 Rounds

[bu08usc11]

Hi Everyone,

I have been trying to figure out how to make this format work and I think it's just something my brain can't put together the right way.

Here is the scenario:

9 Teams, 3 Teams per Round (a Threesome, essentially), 6 Rounds.

Here is the catch, the Teams in a given round are assigned to be Team 1, Team 2, Team 3 and I need every team to be Team 1 twice, Team 2 twice, and Team 3 twice (think everyone playing offense twice, defense twice, and (insert third option) twice). 

I need to set it up where no one plays anyone 3 times in those 6 rounds AND where they do not play the same Team as the same Team position (e.g. Team A cannot play Team B as the same Team1/Team2 matchup) twice. 

This is what I have now but it has 2 3x matchups which I am trying to avoid while keeping the 2x Team 1, 2x Team 2, 2x Team 3 requirement and the not seeing same Team Letter as same Team 1/2/3 side. The below table is by round (6 rounds) and ordered left to right Team 1, 2, 3. 

Team 1/Team 2/Team 3

F A C
G B H
E D I

A E B
H F D
C I G

I H A
F G E
B C D

C E H
B I F
D G A

H D B
I A E
G C F

A F G
E H C
D B I

A - B C D E E F F G G H I I
B - A C D D D E F G H H I I - 3D
C - A B D E E F F G G H H I
D - A B B B C E F G H H I I - 3B
E - A A B C C D F G H H I I
F - A A B C C D E G G G H I - 3G
G - A A B C C D E F F F H I - 3F
H - A B B C C D D E E F G I
I - A A B B C D D E F F G H


Any help would be wonderful in adjusting this setup. 

[Ian Wakeling]

I haven't any software to try to solve this, but doing it by hand I can come close.  They key I think is choosing the first 4 rounds so that every pair of team play together exactly once, then the problem reduces to finding an additional 2 rounds.  This is what I have:

8 7 1
9 3 6
5 2 4

2 8 3
4 9 7
1 6 5

2 1 9
6 4 8
3 5 7

7 6 2
5 8 9
4 3 1

1 4 2
8 7 5
3 9 6

9 5 4
6 1 8
7 2 3

It meets your critera except that pairs (6,8) & (7,8) play twice in the same columns - is that close enough?