Brain Teasers · One Seat in the Boat
Wolf Goat Cabbage Puzzle - The 7-Crossing Answer
The wolf, goat and cabbage river crossing as a story - seven crossings, one backward move.
What is the wolf, goat, and cabbage river-crossing puzzle?
This is one of the oldest documented river-crossing puzzles in Western mathematics, appearing in Propositiones ad Acuendos Juvenes ('Problems to Sharpen the Young'), a collection of puzzles traditionally attributed to the scholar Alcuin of York around the early ninth century. A farmer must ferry three items - traditionally a wolf, a goat, and a head of cabbage - across a river using a boat that only holds him plus one item at a time. Left alone together, the wolf eats the goat and the goat eats the cabbage; the wolf has no interest in the cabbage.
The puzzle is a small, clean example of a constrained search problem: at every point there is a 'state' (who is on which bank), some states are forbidden (any unsupervised pair that would end badly), and the task is to find a sequence of legal moves from the start state to the goal state. It's solvable by hand, but it is also a standard toy example in computer science and AI courses for representing a problem as a graph of states and searching it, decades before 'state-space search' was formal terminology.
What makes it a tricky puzzle is that the obvious approach - ferry each item across once, in some order - never works, because the goat conflicts with both of the other items and can never be left alone with either. The only way through requires bringing an already-delivered item back across the river, which most solvers rule out as a wasted move before they've tried it. The lesson is procedural: identify the item involved in every conflict, and don't assume progress has to be monotonic.
The same structure - one item that conflicts with everything else, a boat or bridge with a capacity limit, and a need for at least one counterintuitive backward step - recurs in many variants with different casts (missionaries and cannibals, jealous husbands, farmers and foxes), all solved by exactly the same state-space reasoning.
How it works
A farmer must ferry a wolf, a goat and a sack of cabbages across a river in a boat that holds him plus one passenger. Left unsupervised, the wolf eats the goat and the goat eats the cabbages; the wolf has no interest in cabbage. He may cross as often as he likes in either direction. The story asks how he gets all three across intact. You lock in a guess, then step through the answer and breakdown.
How scoring works
No grading - your guess is displayed back beside the answer. The story teasers share one lifetime unlock for free users.
The key insight
The goat appears in both conflicts while the wolf and cabbage are safe together, so the goat crosses first and can never be left with either of the others. Keeping that invariant true mid-puzzle forces the non-obvious move: after delivering the wolf, the farmer brings the goat back. Seven crossings total, and the lesson is that progress in a constrained search is not monotone - the 'no backward moves' rule is one solvers invent themselves.
The full step-by-step solution lives at /brain-teasers/river-crossing/solution.
A worked example
Goat over, back empty, wolf over, goat BACK, cabbage over, back empty, goat over - seven crossings. Taking the cabbage third instead of the wolf works symmetrically; refusing to let anything ride back never works.
Common mistakes
• Assuming each passenger crosses exactly once - the rule that makes the puzzle look impossible is one you added yourself.
• Searching moves at random instead of identifying the goat as the piece in every conflict.
• Declaring it unsolvable after three moves instead of questioning the invented constraint.
Why interviews test this
As an interview question this is a state-space search in disguise: interviewers listen for the invariant, the goat never unsupervised with anything, and a memorised sequence does not show it. The written solution is at /brain-teasers/river-crossing/solution.
Play One Seat in the Boat on Outcry
One Seat in the Boat is free to play on Outcry, in the Brain Teasers section, and every run is timed and scored. Read the guide once, then play One Seat in the Boat and check your score against the strategy above. The guide book has a written guide for every other game, and the practice hub and mock assessments put the same skills under a real screen's clock.