Propositiones ad Acuendos Juvenes/Problems/43 - De Porcis/Also presented as

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

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?


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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