River Crossing Puzzle

In a river-crossing puzzle everyone has to get across in a small boat, and some of them cannot be left together. This sets out each puzzle's rules exactly: who can row, how many the boat holds, and who may not be left with whom. It then searches every arrangement that can arise, so it can say whether the crossing is possible, the fewest crossings it takes, and how many different shortest ways there are. Play it here with undo, or print a worksheet with the solution on its own page.

Puzzle

Farmer, wolf, goat and cabbage. Traditional puzzle. Traditional: it is recorded about the year 800 in the Latin puzzle collection Propositiones ad acuendos juvenes.

Everyone starts on the left bank with the boat. The boat holds 2, and someone who can row must be in it: only the farmer can row.
After each crossing, on both banks, the wolf and the goat may not be together without the farmer. Those just arriving count on the bank they arrive at.
After each crossing, on both banks, the goat and the cabbage may not be together without the farmer. Those just arriving count on the bank they arrive at.
Get everyone to the right bank.

Solvable. The fewest crossings is 7, and there are 2 different shortest solutions (a solution here is the list of who crosses each time). This comes from searching all 10 arrangements reachable from the start.

Left bank (boat here): the farmer, the wolf, the goat and the cabbage

Right bank: nobody

Who crosses now?

the farmer

the wolf

the goat

the cabbage

The shortest solutions

All 2, each 7 crossings:

the farmer and the goat →; the farmer ←; the farmer and the cabbage →; the farmer and the goat ←; the farmer and the wolf →; the farmer ←; the farmer and the goat →
the farmer and the goat →; the farmer ←; the farmer and the wolf →; the farmer and the goat ←; the farmer and the cabbage →; the farmer ←; the farmer and the goat →

Paper size

Print size

Margin

Millimetres of blank edge, 5 to 40.

Turn the paper sideways

How to print this, or save it as a PDF

There is no PDF to download, and there does not need to be. Open the print command in your browser and choose “Save as PDF” as the destination. Your browser decides whether the page address and date print across the top and bottom; if they appear, turn off “Headers and footers” in the print dialog.
Set the scale to 100%, not “fit to page”. This sheet is already the exact size of the paper you chose, so anything that resizes it makes every measurement on it wrong.
Leave the paper size in the dialog set to the same one you chose here.

Farmer, wolf, goat and cabbage. Traditional puzzle. Everyone starts on the left bank. The boat holds 2; someone who can row must be in it. On both banks, the wolf and the goat may not be together without the farmer. On both banks, the goat and the cabbage may not be together without the farmer. Get everyone across in as few crossings as you can. It can be done in 7.

Crossing	Who goes	Left bank after	Right bank after
1 →
2 ←
3 →
4 ←
5 →
6 ←
7 →
8 ←
9 →

1 of 2

One shortest solution (7 crossings; there are 2 shortest solutions in all)

1 →	the farmer and the goat	the wolf and the cabbage	the farmer and the goat
2 ←	the farmer	the farmer, the wolf and the cabbage	the goat
3 →	the farmer and the cabbage	the wolf	the farmer, the goat and the cabbage
4 ←	the farmer and the goat	the farmer, the wolf and the goat	the cabbage
5 →	the farmer and the wolf	the goat	the farmer, the wolf and the cabbage
6 ←	the farmer	the farmer and the goat	the wolf and the cabbage
7 →	the farmer and the goat	nobody	the farmer, the wolf, the goat and the cabbage

2 of 2

What this generator does

Models each puzzle as kinds of passenger, the boat's seats, who can row, and rules about who may not be left together. An arrangement is how many of each kind are on the left bank and which side the boat is on, so every arrangement can be listed. A breadth-first search from the start then finds the fewest crossings and counts every shortest solution; when the far bank cannot be reached, it says how many arrangements it went through before running out.

How to use this tool

Choose a puzzle; for shepherds and wolves, choose how many pairs and how many seats the boat has.
Tick who crosses and press Cross. A crossing that breaks a rule is refused with the reason.
Undo or start again at any time, open the shortest solutions, or print the worksheet and a solution.

Understanding the controls

Puzzle: Farmer, wolf, goat and cabbage (traditional); a picnic and a garden (written for this site); or shepherds and wolves, the traditional numbers rule on our own theme.
Pairs and boat seats: For shepherds and wolves: 1 to 6 pairs and a boat for 2, 3 or 4. Some settings are impossible, and the page shows why.
Who crosses now?: Tick who goes, or choose how many of each. Someone who can row must be aboard.

Worked examples

Farmer, wolf, goat and cabbage: 7 crossings, and exactly two shortest ways: take the goat over, come back, take the wolf (or the cabbage), bring the goat back, take the cabbage (or the wolf), come back, take the goat.
Shepherds and wolves, boat for 2: 1 pair: 1 crossing. 2 pairs: 5. 3 pairs: 11. 4 or more pairs: impossible, however the crossings are arranged.

Common use cases

A classic logic puzzle for a class, with the rules written out and the fewest crossings known
Comparing settings: why three pairs of shepherds and wolves can cross in a boat for two and four pairs cannot
A printable worksheet with a table to fill in and the solution separate

How this generator works

After every crossing both banks are checked, and the passengers who have just arrived count on the bank they reach. A move is allowed if the boat carries between one passenger and its full number of seats, including someone who can row, and both banks then obey every rule. Breadth-first search visits arrangements in order of how many crossings they take, so the first time it reaches everyone across is the fewest possible; counting the ways into each arrangement gives the number of shortest solutions. A separate check replays solutions with every person named and the rules tested in words, and a second, deepening search confirms each minimum in the tests.

Randomness and fairness

Nothing here is random: each puzzle is fixed, and the same settings always give the same analysis.

For how randomness is produced across the whole site, see how Generate Random works.

Assumptions this tool makes

The rules apply on the banks, not in the boat, and someone must row every crossing, including the way back.

Limitations and good to know

Four puzzle families only; you cannot write your own rules here.
Shortest is counted in crossings; time, distance and who rows are not weighed.
When there are many shortest solutions, the first twelve are listed and the rest are only counted.

Common mistakes

Forgetting that the boat needs a rower to come back: Every return trip needs someone who can row, which is why the farmer crosses so often.
Thinking the goat can never come back: Bringing the goat back is the key move in the traditional puzzle.

Privacy and your data

Puzzles run in your browser. With analytics consent, a count records how many crossings were made; your moves are not sent.