Pairing Riddle (OT)

[LanX]

off topic (but still graph theory)

I've heard of a case where a woman married her direct uncle.¹

Now I started wondering:

Is it legally possible that she is also his direct aunt?

I don't think so, but I can't wrap my head around it ...

• "Direct" means blood related, i.e sibling of one parent, not "uncle by marriage".
• "Legal"° means without incestuous implications of the pair or their relatives (in western societies)

(FWIW marrying your cousin counts as legal, like in most western* countries, the taboo stems from medieval Catholic church law)

*) surprisingly many US states don't fall under my western definition - > Cousin marriage

°) turns out laws are so inconsistent, that I need to define it:

German rules:

• no marriage with direct descendant (Mother, Father, Grandparent, Great-Greatparent,...)
• no marriage between siblings or half-siblings ((Half-)Brother, (Half-)Sister)

Spoiler Update

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Updates

¹) since I've been asked: this was a Jewish marriage in Cairo/Egypt. In the Middle East marriages are mostly regulated by the communities, and apparently it's not a taboo in Judaism. Avunculate marriage lists another (again Jewish) case in New York, which was upheld in court.

As always you'll also find many examples in the pedigrees of royal houses, like the Windsors.

[LanX]

Given the down votes it attracted, it might have been better to motivate it with breeding dogs to avoid touching on taboos.° =)

But I enjoyed it from a mathematical perspective, since it's a a problem which can be perfectly described in graph theoretic terms: a directed graph with a "child of" relation with certain restrictions:

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Here the solution in short, but hidden behind a spoiler tag to protect those interested.

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°) apparently do most so called "purebred" dogs have an inbreeding factor of 25%. That's like the outcome of incest. One more reason why I'd always opt for a mongrel.

¹) in some western countries this is technically legal, because the laws don't cover that case.

[Ratazong]

Hi LanX, there is another possibility not mentioned in your spoiler:
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seems to be much easier than originally thought ... but does not involve any graph-theory ...

So long, Rata

[LanX]

Thanks, Rata. But I think you missed the requirement in the OP that uncle/aunt by marriage doesn't count.

> > > "Direct" means blood related, i.e sibling of one parent, not "uncle by marriage".

In hindsight it becomes clearer why breeding dogs would be a better setting for this puzzle.

Dogs don't know marriage, divorce and soap operas° ... ;)

And many breeders rely on incest, restricting them to uncle/aunt relationships would be a "moral" advantage.

Update

The trivial solution (of many) if "by marriage" was allowed ...

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°)

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