Propositiones ad Acuendos Juvenes/Problems/41 - De Sode et Scrofa

Propositiones ad Acuendos Juvenes by Alcuin of York: Problem $41$

A farmer created a new yard in which he put a breeding sow,

which produced a litter of $7$ piglets in the centre,

which with their mother makes $8$.

They all bear litters of $7$ piglets each in the first corner of the yard,

then all of them bear litters of $7$ piglets each in the next corner

and so on for all corners.

Finally they all bear litters of $7$ in the centre pigsty.

How many pigs are there now altogether, including the mothers?

$262 \, 144$.

At the first birth, in the centre pigsty, there are $7$ piglets with the mother, making $8$.

In the first corner there are $8 \times 8 = 64$.

In the second corner there are $64 \times 8 = 512$.

In the third corner there are $512 \times 8 = 4096$.

In the fourth corner there are $4096 \times 8 = 32 \, 768$.

Multiplying this by $8$ gives $262 \, 144$.

This gives the total number of pigs after the final litters are produced in the centre pigsty.

Hence the result.

$\blacksquare$

First it is noted that all the piglets born must be female in order to have litters of their own.

The method of impregnation has also not been considered, but that is a mere detail.

What is interesting is that Alcuin makes a mistake in his arithmetic, calculating $32 \, 788$ as the number of pigs in the fourth corner.

This mistake is propagated to the final quantity of pigs, which he gives as $262 \, 304$.

Arithmetic clearly continues to be difficult throughout history, as translations through the ages give several different wrong results.

It is also noted that the word sode is not a standard Latin word, but all the texts have it.