Propositiones ad Acuendos Juvenes/Problems/53 - De Homine Patrefamilias Monasterii XII Monachorum
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Propositiones ad Acuendos Juvenes by Alcuin of York: Problem $53$
- De Homine Patrefamilias Monasterii $\text {XII}$ Monachorum
- An Abbot with $12$ Monks
- An abbot had $12$ monks in his monastery.
- Calling his steward he gave him $204$ eggs and ordered that he give equal shares to each monk.
- Thus he ordered that he give:
- $85$ eggs to the $5$ priests,
- and $68$ to the $4$ deacons
- and $51$ to the $3$ readers.
- How many eggs went to each monk, so that none had too many or too few,
- but all received equal portions as above?
Solution
$17$.
Proof
Take the $12$th part of $204$.
This $12$th part is $17$, so $204$ is $12$ times $17$ or $17$ times $12$.
Just as $85$ is $5$ times $17$, so is $68$ four times and $51$ three times.
Now $5$ and $4$ and $3$ are $12$.
There are $12$ men.
Again add $85$ and $68$ and $51$ which is $204$.
There are $204$ eggs.
Therefore to each comes $17$ eggs as the $12$th part.
$\blacksquare$
Historical Note
It is suggested that this problem has been corrupted.
It feels as though it ought to be a one hundred fowls problem, but the answer is provided as part of the question.
The answer looks as though the scribe is bewilderedly wondering if it be a trick question.
Compare it with Problem $47$: De Episcopo qui Jussit XII Panes in Clero Dividi.
Sources
- c. 800: Alcuin of York: Propositiones ad Acuendos Juvenes ... (previous)
- 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