# Propositiones ad Acuendos Juvenes/Problems/6 - De Duobis Negotiatoribus C Solidos Communis Habentibus/Historical Note

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## Historical Note on *Propositiones ad Acuendos Juvenes* by Alcuin of York: Problem $6$: De Duobis Negotiatoribus

According to David Singmaster, this is the first appearance of the type of problem known as the **Applesellers' Problem**, also known as the **missing penny** or **marketwomen's problem**.

It hinges on the fact that a common mean is erroneously being calculated of $2$ for a monetary unit plus $3$ for a monetary unit equals $5$ for $2$ monetary units.

David Singmaster goes on to remark that, while this problem appears everywhere in European puzzle-books since its appearance here, he has never seen a non-European version.

However, Maurice Kraitchik claims in his *Mathematical Recreations* that it appears in Mahaviracharya's *Ganita Sara Samgraha*, which dates from c. $850$. However, this has not been corroborated.

## Sources

- 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