Combination Generation

[nayrb11]

I am wondering if there is a formula or easy way to fix a combination problem I am working on using excel.

Basically, I have 12 numbers (1-12).



I want them in 2 groups of 3 where:

Conditions
1. Each number is in the same group exactly 2 times with every number.
2. Each number is in the opposing group exactly 3 times with every number.
3. No group of 3 is ever repeated.
4. Every number appears an equal amount of times (11 I think is the max/ideal)


For example:

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

Now (1,2),(1,4),(5,6),(3,6),(7,8),(7,10),(11,12) and (9,12) could not be in the same group.
Now 1 and 6, as well as 7 and 12 could not be in opposing groups.

Long story short, randomized teams of 3 that play with everyone and against everyone an equal amount of times.


If it's confusing I can try and explain it further, but any help?

[tuph]

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