river-crossing problems
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The wolf, goat, and cabbage river-crossing problem.
Illustration from the cover of Introduction to the Design and
Analysis of Algorithms by Anany Levitin
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Puzzles in which a variety of objects and living things, some of them mutually
incompatible, must be conveyed in small groups from one side of a river
to another without any loss along the way. The earliest known examples are
in Propositiones ad Acuendos, which is generally attributed to
Abbott Alcuin. They are: the problem of three
jealous husbands (each of whom won't let another man be alone with his wife),
the problem of the wolf, the goat, and the cabbage, and the problem of the
two adults and two children where the children weigh half as much as the
adults. In the wolf-goat-cabbage case, the difficulty is that only one item
can be ferried across at once but, if left unattended, the sheep will eat
the cabbage and the wolf will eat the sheep. The solution, which involves
a stratagem common to all these types of problems, is to bring back to the
starting bank of the river an item that has already been taken across. In
this case, the sheep must be taken across first, followed by either the
cabbage or the wolf, but then the sheep must be brought back before the
next item is taken across to avoid the sheep become either a diner or a
dinner.
These medieval puzzles were considered and elaborated by Niccoló Tartaglia,
Luca Pacioli, and Claude-Gaspar Bachet,
and even more so by later mathematicians such as Edouard Lucas
and Gaston Tarry, and others. Ways of complicating river-crossing problems
include adding more people and objects, using a bigger boat, and inserting
an island in the river.
Related category
• GAMES
AND PUZZLES
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