Propositiones ad Acuendos Juvenes/Problems/18 - De Lupo et Capra et Fasciculo Cauli/Solution 2

Propositiones ad Acuendos Juvenes by Alcuin of York: Problem $18$

A man takes a wolf, a goat and a bunch of cabbages across the river.

The only boat he could find could take only 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?

Solution

The constraints here are that:

$(1): \quad$ The wolf, if left alone with the goat, would eat it, so these two may not be left alone together.

$(2): \quad$ The goat, if left alone with the bunch of cabbages, would eat it, so these two may not be left alone together.

Let $M$, $W$, $G$ and $C$ denote the man, wolf, goat and cabbages respectively.

Let them be crossing from $A$ to $B$.

As follows:

$M$ takes $G$ from $A$ to $B$.

$M$ returns to $A$.

$M$ takes $C$ from $A$ to $B$.

$M$ returns to $A$ with $G$.

$M$ takes $W$ from $A$ to $B$.

$M$ returns to $A$.

$M$ takes $G$ from $A$ to $B$.

Sources

• 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