Propositiones ad Acuendos Juvenes/Problems/53 - De Homine Patrefamilias Monasterii XII Monachorum

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?

$17$.

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.

$\blacksquare$

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.