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I am looking for an algorithm which can determine a schedule of games to be played given the following parameters.

- There are 12 teams in the league
- There are 4 venues
- Every Wednesday for 11 weeks, each team plays 2 other teams at one of the specified venues; thus each team will play 22 matches in the season
- Every team must play every other team exactly twice throughout the season

Essentially, you just need to group the teams in blocks of 3 each week such that they only appear in the same group as another team twice in the season.

Here would be an example of the first couple weeks:

Week 1: Venue A: 1,2,3; Venue B: 4,5,6; Venue C: 7,8,9; Venue D: 10, 11, 12
Week 2: Venue A: 1,5,9; Venue B: 2,6,10; Venue C: 3,7,11; Venue D: 4, 8, 12
.
.
.
Week 11: ?

Testing all the combinations is obviously not feasible. Any help would be greatly appreciated.
Posted 8-Mar-13 2:56am
Updated 8-Mar-13 3:50am
v2
Mike Meinz 8-Mar-13 9:29am

Do you mean "Round Robin"?
MichaelBergsma 8-Mar-13 9:50am

Yes, yes I do.
Sandeep Mewara 8-Mar-13 11:06am

What are your thoughts? Tried anything so far?
MichaelBergsma 8-Mar-13 11:54am

I read througth http://en.wikipedia.org/wiki/Round-robin_tournament and tried a modified version of the diagonal scheme but since I need teams to be group in three instead of 2, it makes it more difficult.
MichaelBergsma 8-Mar-13 13:02pm

I didn't realize what a can of worms this was.

http://en.wikipedia.org/wiki/Steiner_system
http://en.wikipedia.org/wiki/Kirkman's_schoolgirl_problem
http://demonstrations.wolfram.com/SocialGolferProblem/

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