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I'm not even sure how to word this question. So I'll explain it out.

I've got these values:

$A_1, A_2, B_1, B_2, B_3, C_1, C_2$,

I need

  • each $A$ to be paired with each $B$ and $C$
  • each $B$ with each $A$ and $C$
  • each $C$ with each $A$ and $B$

but they can only be paired with one other letter at a time (i.e. in one day).

Each permutation is exclusive, meaning when $A_1$ is paired with $B_1$. $A_2$ could be paired with $B_2$ or $B_3$ or $C_1$ or $C_2$ but not $A_1$.

But as many as possible need to be paired at the same time.

If I put that into the real world each number could represent a person and the letters represent a skill. On a Monday I want two people with each skill to work with each other and as many people as possible to be working together. In a rotational system every day until the first two people are pairing again.

So hopefully I could come up with some table that would show who is working with who when.

Mon | Tues | ..

$A_{1}B_{1} | A_{1}B_2 |$
$A_{2}B_2 | C_{1}A_2 |$

Is this possible, what is the name of the type of algorithm this is formed from?

Also what is the answer :-)

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    Actually, pairwise coverage would mean that you want tuples A_i B_j C_k.2012-03-15

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