Propositiones ad Acuendos Juvenes/Problems/6 - De Duobis Negotiatoribus C Solidos Communis Habentibus
Propositiones ad Acuendos Juvenes by Alcuin of York: Problem $6$
- De Duobis Negotiatoribus $\text C$ Solidos Communis Habentibus
- $2$ Wholesalers with $100$ Shillings
- $2$ wholesalers with $100$ shillings between them bought some pigs with the money.
- They bought at the rate of $5$ pigs for $2$ shillings, intending to fatten them up and sell them again, making a profit.
- But when they found that it is not the right time of year for fattening pigs,
- and they were not able to feed them through the winter,
- they tried to sell them again to make a profit.
- But they couldn't, because they could only sell them for the price they had paid for them, $2$ shillings for $5$ pigs.
- When they saw this, they said to each other, "Let's divide them.
- By dividing them, and selling them again at the rate they had bought them for, they made a profit.
- How could they be divided to make a profit, which could not be made by selling them all at once?
First there were $250$ pigs bought with $100$ shillings at the above mentioned rate, for $5$ fifties are $250$.
On division, each merchant had $125$ pigs.
One sold the poorer quality pigs at $3$ for a shilling.
The other sold the better quality pigs at $2$ for a shilling.
The one who sold the poorer quality pigs received $40$ shillings for $120$ pigs.
The one who sold the better quality pigs received $60$ shillings for $120$ pigs.
Then there remained $5$ of each sort of pig.
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.
- 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
- 1992: David Wells: Curious and Interesting Puzzles ... (previous) ... (next): 'Propositions to Sharpen Up the Young': $77$