Propositiones ad Acuendos Juvenes/Problems/43 - De Porcis

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Propositiones ad Acuendos Juvenes by Alcuin of York: Problem $43$

De Porcis
A puzzle of pigs
A man has $300$ pigs, and orders that the pigs must be killed,
an odd number each day,
in $3$ days.
How many pigs should be killed each day?


Solution

In the words of Alcuin of York:

This is a fable.
No-one can solve how to kill $300$ pigs in $3$ days, an odd number each day.
This fable is given to children.


Modern interpretations can produce answers along the lines:

$1$ on the first day, $1$ on the second day, and $298$ on the third day.
$298$ is a very odd number of pigs to kill in one day.

As such, this is a fallacy of equivocation:

odd meaning either an odd number as opposed to an even number
odd meaning unusual or strange.


Also presented as

Some sources present this problem with the number of pigs being set to $30$.

The answer is the same.

You cannot add $3$ odd numbers and reach $30$.


Historical Note

The question is raised in some sources as to whether this problem can be construed as cruelty to children.

Some suggest that Alcuin may have used this problem to distract the more rambunctious of his pupils.

In any event, this is an early recognition that there exist problems which have no solution.


A more subtle variant on the problem has arisen in more recent years: dividing an odd number of pigs into pens into an even number of pens so that is an odd number of pigs in each pen.

The problem is solved by housing them in concentric pens, for example: $3$ pigs can be partitioned into $2$ pens with one pig in the inside pen, and $2$ in the outside pen.


Sources

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