Solution
Wolf, Goat, and Cabbage
Show the problem again
A farmer must ferry a wolf, a goat, and a cabbage across a river in a boat holding only himself and one item. Left unattended together, the wolf eats the goat and the goat eats the cabbage. What is the minimum number of river crossings needed to get everything across safely?
Worked solution
The answer is 7 crossings. Take the goat over (1), return empty (2), take the wolf over (3), bring the goat back (4), take the cabbage over (5), return empty (6), take the goat over (7). The key insight is that items may be brought back; the goat, the only item dangerous in both pairings, shuttles.
Source: From Alcuin of York, 'Propositiones ad Acuendos Juvenes' (c. 800). Statement written for AxiomIQ.