Propositiones ad Acuendos Juvenes/Problems/43 - De Porcis/Historical Note

Historical Note on Propositiones ad Acuendos Juvenes by Alcuin of York: Problem $43$: De Porcis

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

• c. 800: Alcuin of York: Propositiones ad Acuendos Juvenes
• 1992: John Hadley/2 and David Singmaster: Problems to Sharpen the Young (Math. Gazette Vol. 76, no. 475: pp. 102 – 126)  www.jstor.org/stable/3620384
• 1992: David Wells: Curious and Interesting Puzzles ... (previous) ... (next): 'Propositions to Sharpen Up the Young': $76$