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