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 :-)