Propositiones ad Acuendos Juvenes/Problems/11 - De Duobus Hominibus Singulas Sorores Accipientibus/Variant 2

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Propositiones ad Acuendos Juvenes by Alcuin of York: Problem $\text {11 b}$

De Patre et Filio et Vidua Eiusque Filia
A father and son and a widow and her daughter
If a relict or widow and her daughter take a father and son in marriage,
so that the son marries the mother and the father marries the daughter,
what is the relationship of their sons?


Solution

Each son is simultaneously the nephew and the uncle of the other.

Let son $1$ be the son of Father and Daughter.
Let son $2$ be the son of Son and Mother.

Then:

$(1): \quad$ Son $1$ and Son are both the sons of Father, which makes son $1$ the uncle of son $2$

and at the same time:

$(2): \quad$ Son $2$ and Daughter are both the children of Mother, which makes son $1$ the nephew of son $2$

and vice versa.


Historical Note

According to David Singmaster, this problem, along with two related problems (no pun intended) originating from Bede which he also documents, are the earliest of the strange family type.


There are contemporary examples of such:

At 52, Rolling Stones bassist Bill Wyman married 18-year-old Mandy Smith but divorced after a year.
Bill's 30-year-old son then, Stephen married Mandy's mother, age 46.
Therefore, Bill became the father-in-law of his ex mother-in-law
as well as the stepgrandfather of his former wife.


Sources

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