Propositiones ad Acuendos Juvenes/Problems/21 - De Campo et Ovibus in Eo Locandis

Propositiones ad Acuendos Juvenes by Alcuin of York: Problem $21$

De Campo et Ovibus in Eo Locandis

Sheep in a Field

There is a field $200$ feet long and $100$ feet wide.

I want to put sheep in it, so that each sheep has $5$ feet by $4$.

How many sheep can I put in there?

Solution

$1000$.

Proof

We have that:

$5$ goes into $200$ a total of $40$ times

$4$ goes into $100$ also a total of $25$ times.

Thus we can put $40 \times 25 = 1000$ sheep into that field.

$\blacksquare$

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