Propositiones ad Acuendos Juvenes/Problems/52 - De Homine Patrefamilias/Historical Note

Historical Note on Propositiones ad Acuendos Juvenes by Alcuin of York: Problem $52$: De Homine Patrefamilias

David Singmaster suggests that the camel does in fact make $4$ journeys, not $3$.

However, $\mathsf{Pr} \infty \mathsf{fWiki}$ contend that the $3$rd journey to carry $30$ measures $20$ leucas, then $30$ leucas the remaining $10$ leucas, is in fact one journey, just broken into $2$ parts.

It is suggested that there may be a further unspoken constraint given here: that a camel may not be able to carry more than $30$ measures at one time.

Note also that the camel does not require food when he is not carrying a load.

There exists a better solution if more than $3$ trips are allowed:

The camel makes $3$ trips carrying $30$ measures to $10$ leucas, there now being $60$ measures at $10$ leucas.

The camel makes $2$ trips carrying $30$ measures to a point another $15$ leucas further, there now being $30$ measures $25$ leucas on.

The camel makes $1$ further trip of $5$ leucas carrying those $30$ measures to the destination, eating $5$ and so carrying $25$ measures in total.

This may be the earliest appearance of a desert crossing problem.

Sources

• c. 800: Alcuin of York: Propositiones ad Acuendos Juvenes
• 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