Erich Prisner

Wolf, goat, cabbage, ...

Difficulty Level 1: You want to transfer wolf ("W"), goat ("G"), and cabbage ("C") from the left bank of the river to the right bank. You, the only human there, are the rower, and don't leave the boat. The wolf wants to eat the goat, the goat wants to eat the cabbage, but nothing will happen as long as you are near. Beside you there is only place for one item in the boat. How can you achieve your task? Click on "W", "G", or "C" to put them in or out of the boat. Click the boat to get it moving.

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In this puzzle you can hardly do anything wrong as long as you obey the rule

Never do something to get a situation you had already before.

The only possible first move is to ship the goat, "G", to the right. Shipping it back would violate our rule, therefore we go back with an empty boat. We may not go empty to the right (we would violate the rule). therefore we take "W" or "C", which one really doesn't matter, the situation is symmetric, so let's say "W" moves. Now we have to take something back, but not "W" (remember our rule), so we ship "G" to the left. Next we ship "C" to the right. Here is the only state where you could do something wrong by shipping "W" to the left---instead we row with an empty boat to the left, pick up "G", and ship to the right.

Variants: More items to move

The puzzle being so simple, one might ask: Can we change it to make it more complicated? What happens if we have to move a school class? You can formulate the instance of your problem in the setup phase---everything you do before clicking on the word "Start"--- as follows:

In the first phase you generate your problem. Click on some of the letters shown in the red box to get them on the left bank. You may move letters back into the red box in this phase by clicking on it.
The boat size is initially 2. Adjust it to 1 by clicking on "decrease size".
Now click on the word "Start". The red box disappears, and you can play.

After clicking "Start" you are in the playing phase. Try to move the students from the left bank to the right bank by clicking as before. Note that adjacent students would fight, so you can not leave students standing directly adjacent on the bank you leave.

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Try different initial configurations, but stick to boat size 1.

Question 1: Which of the initial configurations are solvable with a boat of size 1?

Here are links to certain other wolf, goat, cabbage pages in English or German:

English links:

Much nicer applet than mine, where the goat can actually be eaten.
Cut the knot: A nice applet together with the cube graph.
Ask Dr. Math
Problem slightly misstated. Shows the solution in table form
Another program
History and variants
larger boat version

German links:

Erich Prisner, 2002-2004