River Crossing Puzzles
A boat that carries one item, a set of items that cannot be left alone together, and a river to cross. Every puzzle is verified solvable by search, the shortest crossing sequence is known, and each move of it is explained. Sixty puzzles across three conflict layouts, both directions.
Also known as the wolf, goat and cabbage puzzle and river crossing logic.
The Boat Holds One, The Conflicts Hold Everything
A river crossing puzzle gives a set of items with dangerous pairs: items that cannot be left alone together on a bank. The boat carries the traveller plus at most one item. Every crossing changes the state — which items are on each bank, and which side the boat sits on — and a crossing that leaves a conflicting pair alone loses the puzzle.
How To Solve A River Crossing Puzzle
- Name the conflicts. Write down every pair that cannot be left alone. Everything follows from this list.
- Take the item in the most conflicts first. In the classic set, that is the goat — it conflicts with both the wolf and the cabbage.
- Expect to bring items back. The famous seventh move of the classic puzzle is bringing the goat back. Returns are not mistakes; they are the mechanism.
- Audit both banks after every crossing. The bank the traveller left must be conflict-free, and so must the bank just reached.
- Count crossings against par. The board knows the shortest sequence; the par tells you when a route has gone long.
Every puzzle here is proven solvable by search. The generator runs a breadth-first search over all possible states before the puzzle ships, so the shortest solution exists, is verified, and the walkthrough narrates it crossing by crossing.
The Three Conflict Layouts
| Layout | Conflicts | Shortest solution |
|---|---|---|
| Chained conflicts | A–B and B–C | 7 crossings — the classic wolf, goat and cabbage |
| Star conflicts | One item conflicts with both others | 7 crossings, with the troublemaker shuttling |
| Single conflict | One dangerous pair only | 5 crossings — a gentle warm-up |
Learn The Method, Not The Moves
Every item set here comes in both directions: left-to-right and its mirror. The state graph is identical — only the labels flip — so a solver who memorises the moves of one finds the other trivial. The test of the method is the mirror: same conflicts, same crossing count, different moves, one working brain.
River Crossing Puzzles: Frequently Asked Questions
What is the river crossing puzzle?
A traveller ferries a set of items across a river in a boat that carries the traveller plus one item. Some pairs cannot be left alone together. The goal: everything across the river with nothing eaten.
How do you solve the classic wolf, goat and cabbage crossing?
Take the goat across first. Return alone. Take the wolf across and bring the goat back. Take the cabbage across. Return alone, then take the goat. Seven crossings.
What is the minimum number of crossings?
For the classic set, seven. The search over all possible states proves no shorter sequence exists.
Why does the goat have to come back?
The goat sits in both conflicts: the wolf eats it and it eats the cabbage. Bringing it back keeps it separated from both while the other items move.
How many puzzles are there?
There is no fixed number. Each puzzle is rebuilt from the short seed in the page address, so the supply is effectively unlimited. Copying the puzzle link saves that exact puzzle permanently.
Can I practise one pattern at a time?
Yes. Pick any pattern from the catalogue above and the board switches to that item set and direction only, with its own address you can bookmark or hand out.
Are the mirrored puzzles different?
The state graph is identical with the labels flipped. Solving both directions of the same item set tests the method rather than the memory.
Is the river crossing puzzle good for children?
Yes. No arithmetic, one-sentence rules, and immediate visible consequences. One of the best first logic puzzles for ages six and up.