Propositiones ad Acuendos Juvenes/Problems/18 - De Lupo et Capra et Fasciculo Cauli
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Propositiones ad Acuendos Juvenes by Alcuin of York: Problem $18$
- De Lupo et Capra et Fasciculo Cauli
- A Wolf, a Goat and a Bunch of Cabbages
- 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:
Solution 1
- $M$ takes $G$ from $A$ to $B$.
- $M$ returns to $A$.
- $M$ takes $W$ from $A$ to $B$.
- $M$ returns to $A$ with $G$.
- $M$ takes $C$ from $A$ to $B$.
- $M$ returns to $A$.
- $M$ takes $G$ from $A$ to $B$.
- "By this procedure there would be some healthy rowing, but no lacerating catastrophe."
Solution 2
- $M$ 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 $B$.
Also presented as
The objects being transported can be seen presented in various ways, for example:
- fox, duck and grain
- African leopard, goat and cassava leaves
and so on.
$4$ or more objects may be transported in this way, each being incompatible with its two neighbours, but in this case one of the objects needs to be able to row.
Sources
- c. 800: Alcuin of York: Propositiones ad Acuendos Juvenes ... (previous) ... (next)
- 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
- 1992: David Wells: Curious and Interesting Puzzles ... (previous) ... (next): 'Propositions to Sharpen Up the Young': $82$