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.
Sources
- c. 800: Alcuin of York: Propositiones ad Acuendos Juvenes ... (previous) ... (next)
- 1992: John Hadley/2 and David Singmaster: Problems to Sharpen the Young (Math. Gazette Vol. 76, no. 475: pp. 102 – 126) www.jstor.org/stable/3620384