Propositiones ad Acuendos Juvenes/Problems/31 - De Canava

Propositiones ad Acuendos Juvenes by Alcuin of York: Problem $31$

De Canava

A Wine Cellar

There is a wine cellar $100$ feet long and $64$ feet wide.

How many casks will it hold if each cask is $7$ feet long and $4$ feet wide across the middle,

and there is one path $4$ feet wide?

Solution

There are $14$ sevens in $100$, and $16$ fours in $64$.

But $4$ of those $64$ feet must be taken up by the path that runs the length of the cellar.

This leaves $60$ feet and there are $15$ fours in $60$.

Take $15$ times $14$ which is $210$.

That is the number of casks of the given length which can be contained in the wine cellar.

Sources

• c. 800: Alcuin of York: Propositiones ad Acuendos Juvenes ... (previous) ... (next)
• 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