# 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.