Bowling: 12 players(2 teams), 6 lanes

[ReSiStAnCe]

Hi, 
I'm having a problem constructing a schedule for the following:

We have 2 teams with 6 players each. We also have 6 lanes with a different oilpattern. 
Each member of each team has to play against each member of the other team, every game on a different lane.
So if player A1 played player B1 on lane 1 then neither player shall play on lane 1 again, or against each other.
Hope this make some sense..
I do have a schedule for 2 teams / 5players / 5 lanes, and it looks like this:

 
I can't seem to expand this to 6...

Please help..

[Ian Wakeling]

It may come as a surprise that while this works for 5 lanes and 5 games, it is actually impossible for 6 lanes and 6 games.  This was a celebrated mathematical problem known as Euler's 36 officers.  If you follow the link, then it is presented slightly differently, but it is an equivalent problem where the 36 officers represent the 36 games you want to play, A1 to A6 could be the regiments, and B1 to B6 the ranks.

In the best possible solution, one of the two teams will be balanced, but the other team will have two members who play twice on one lane, and not at all on another lane.   Did you find something like that?

[ReSiStAnCe]

Thank you for your swift reply.
I did find something similar. I started out with a simple rotation, which (with some tinkering) worked out good for the first 4 games.
Now I will have some players play each other twice, since it's the lane conditions which provide the challenge.

[Ian Wakeling]

In that case, I think there will have to be two pairs of players who both play each other twice.  If you have more than 2 pairs, then I can make an example schedule.

[ReSiStAnCe]

If you have one at hand, please do. Seems not so straightforward after all..

[Ian Wakeling]

I think this schedule will work

(A5 B1) (A6 B2) (A3 B5) (A4 B6) (A1 B3) (A2 B4) (A2 B6) (A1 B5) (A6 B1) (A5 B2) (A3 B4) (A4 B3) (A6 B4) (A5 B3) (A1 B6) (A2 B5) (A4 B1) (A3 B2) (A4 B5) (A3 B6) (A5 B4) (A6 B3) (A2 B2) (A1 B1) (A1 B2) (A4 B4) (A2 B3) (A3 B1) (A5 B5) (A6 B6) (A3 B3) (A2 B1) (A4 B2) (A1 B4) (A6 B6) (A5 B5)

The repeated games are all in the lower right hand 2x2 square, so it is probably best to reorder the rounds to keep the repeated games as far apart as possible.