Alcuin’s River Puzzles

The ecclesiastic, scholar, writer and poet, Alcuin of York (735-804), produced his puzzle book for the Emperor Charlemagne, possibly the first ever-written. It was called Propositiones ad acuendos juvenes or ‘Puzzles to Sharpen the Young’. These three puzzles, propositions 17, 18 and 19 in the book, are all river crossing puzzles; the first is well-known, the others less so.

Homo quidam debebat ultra fluuium transferre lupum, capram, et fasciculum cauli. Et non potuit aliam nauem inuenire, nisi quae duos tantum ex ipsis ferre ualebat. Praeceptum itaque ei fuerat, ut omnia haec ultra illaesa omnino transferret. Dicat, qui potest, quomodo eis illaesis transire potuit?

This is roughly what the Latin says.

“A man had to carry a wolf, a goat, and a bunch of cabbage[s] across the river. And he could find no other ship, except such as was capable of carrying only two of them. He had therefore been ordered to transfer all these beyond unharmed. Let him who can, say how could he pass through them unscathed?”

To make it clear, he mustn’t leave the goat alone with the cabbages or the wolf alone with the goat, for obvious reasons. How many times would he need to cross the river from one side to the other in order to carry out his task?

Three men each with an unmarried sister wish to cross the river in the same two-seater boat. However Alcuin says each man “had lust for his neighbour’s sister”. More tactfully let’s say a sister would be in a compromising position if her brother was not with her at all times. Hint: Any man or woman can row the boat. Now how many times would the boat need to cross the river, either way, to ferry all the group across the river with decorum?

A man and a woman with their two children want to cross the river. The man and woman weigh the same and each child is half the weight of an adult. The boat can carry two people but can only hold the weight of one adult or it would sink. (Obviously a different boat to that used earlier.) Hint: Both the children can also row. How many times would the boat need to cross the river, either way, to carry the family across the river?


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