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

by : Problem $41$

 * De Sode et Scrofa: A Breeding Sow and a Pigsty
 * 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?

Solution

 * $262 \, 144$.

Proof
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.