# Applesellers' Problem/Historical Note

## Historical Note on the Applesellers' Problem

According to David Singmaster, this type of problem first appeared in *Propositiones ad Acuendos Juvenes* by Alcuin of York, in $800$ CE.

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.

Maurice Kraitchik, on the other hand, includes it in his *Mathematical Recreations* of $1960$ under the heading *Hindu Problems*.

David Wells, who includes Kraitchik's version in his *Curious and Interesting Puzzles* of $1992$, notes that this was taken by Kraitchik from a theme in Mahaviracharya's *Ganita Sara Samgraha*, which dates from c. $850$.

However, this has not been corroborated, and it remains to be identified where in that source it was obtained.

## 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 - 1992: David Wells:
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