River Crossings
Puzzles about taking people, animals, bird s and other items across a river have been popular for hundreds of years. Some of the earliest appeared in the collections called, in Latin, Propositiones ad Acuendos Juvenes or, in English, Problems to Sharpen the Young attributed to Alcuin of York (732 – 804) (translated and annotated by John Hadley and David Singmaster). First we give one of the original Alcuin problems.
PROBLEM 1 A wolf, a goat and a cabbage
A man had to take a wolf, a goat and a cabbage across a river. The only boat he could find could only take two of them at a time. But he had been ordered to transfer all of these to the other side in good condition. How could this be done?
Here is another problem, a little harder than the first.
PROBLEM 2 AliensA tour guide is looking after a party of alien visitors – a Trian, a Quadran and a Pentan. They all have to cross a river using a small boat, only big enough for the guide and one passenger. Trians and Pentans are harmless vegetarians, but the Quadran is a fierce carnivore. How many times does the guide have to row across the river? (You may asssume that the guide will be safe alone with the Quadran.) |  |
This is another of Alcuin’s original problems
 | PROBLEM 3 Three friends and their sisters. Three friends, each with a sister, needed to cross a river. Each one of them desired the sister of another. At the river, they found only one small boat, in which no more than two of them could cross at a time. How did they cross the river without any of the women being defiled by the men? Alcuin’s solution involves 11 crossings but assumes a sister must be with her brother or only other women. |
Pat Perkins
