Basketball Schedule

I've been wracking my brain on this one.

I'm in charge of a basketball league with 12 teams. The league lasts 6 weeks. There are 4 locations where there will be 3 teams each week. At each location there will be 3 games every week. Each team will have 12 games total. There has to be a way in which each team plays every other team and only plays one team twice.

For example:

Week 1 would look like this:

Court 1: 1v.2 1v.3 2v. 3
Court 2: 4v.5 4v.6 5v.6
Court 3: 7v.8 7v.9 8v.9
Court 4: 10v.11 10v.12 11v.12

So 6 weeks, 12 teams, 4 locations with 3 teams apiece, everyone plays everyone else at least once.

Help please!

I haven't got a proof, but I doubt that is possible.

There are 66 matches in which those 12 teams will play each other once, given by (using letters to denote the teams:

A B
A C
A D
A E
A F
A G
A H
A I
A J
A K
A L
B C
B D
B E
B F
B G
B H
B I
B J
B K
B L
C D
C E
C F
C G
C H
C I
C J
C K
C L
D E
D F
D G
D H
D I
D J
D K
D L
E F
E G
E H
E I
E J
E K
E L
F G
F H
F I
F J
F K
F L
G H
G I
G J
G K
G L
H I
H J
H K
H L
I J
I K
I L
J K
J L
K L

Each week there will be 3 matches at each venue, so for 4 venues that means 12 matches, and so over 6 weeks there are potentially 72 matches. However, in arranging the teams each week, you may find that a duplicate match has to be played, so it doesn't necessarily follow that those 66 matches can be fitted into the 72 slots available.

I would suggest that you make up a table like this:

Court_1 A B C
Court_2 D E F
Court_3 G H I
Court_4 J K L

for week 1, and then in the list above mark off those matches using a particular colour (e.g. yellow for A vs B, A vs C, B vs C, and so on for 12 matches). Then for week 2 you may have an arrangement like this:

Court_1 A E I
Court_2 B F J
Court_3 C G K
Court_4 D H L

and then you can mark those matches off in another colour, and then continue this for the other weeks. During the 4th week you will encounter some matches that have been played before, so you just need to minimise the number of these.

I can't think of a way of automating this.

Hope this helps.

Pete

Thanks guys. You would think that with such numbers it would work out - but it sure doesn't. Thanks for your help!