Alcuin, Puzzle-master

Is there anyone who hasn't heard the puzzle of the fox, the goose, and the bag of corn? A man has to transport these three things across a river in a boat which can hold him and one other item. His constraints are that he cannot leave the fox and goose together, or the goose and corn together. This is one of several river-crossing puzzles that exist in different cultures. The earliest version we know of in print is in a late 9th century Latin manuscript of the work Propositiones ad Acuendos Juvenes (Problems to Sharpen the Young), attributed to Alcuin of York (c.735-804).*

"Alcuinus abba"=Father Alcuin

Educated in the cathedral school of York, Alcuin became a monk and teacher. On his way back to England from a trip to Rome in 781 he met Charlemagne, King of the Franks, who recognized Alcuin's erudition and invited him to stay and help promote learning to a level unknown since Rome.

Alcuin became head of the palace school at Aachen, where he established a great library, revised the liturgy, wrote treatises and poetry and works on grammar. It is his influence on learning that is said to have vaulted Latin into the position of being the academic language.

Propositiones ad Acuendos Juvenes is attributed to Alcuin, because of its date and because it is the kind of work he would have created for the pupils at Aachen. The 50+ puzzles in it are very mathematical, with three river-crossing problems—although in his early example the items are a wolf, a goat, and a cabbage. Solutions are provided for all the problems.

Or almost all. There is one that has no solution offered, and it goes like this:

A certain man has 300 pigs. He ordered all of them slaughtered in 3 days, but with an uneven number killed each day. What number were to be killed each day? (Problem 43)

There can be no solution to this puzzle, for obvious reasons. (Feel free to post the reason why in the comments to explain it to your fellow readers.) The assumption is that it was given to difficult students to frustrate them.

*Alcuin also recorded the destruction of Lindisfarne.