Can you help the boatman? (PUZZLE)

01 Apr Can you help the boatman? (PUZZLE)

Puzzles go back centuries. One of the most well-known puzzles is the ‘wolf, the goat and the cabbage’ puzzle that dates back to at least the 9th century. Known also as the ‘fox, chicken and grain puzzle’, ‘the fox, goose and bag of beans puzzle’, ‘the panther, pig and porridge puzzle’ and many other versions, it can be found in many folklores from Africa, to Asia, to Europe, America and Australia.

The puzzle is as follows. A farmer goes to market and buys a wolf, a sheep and a cabbage. On his way home, he has to cross a river by boat from one side to the other. The boat can carry only the farmer and one other thing – the wolf, the goat or the cabbage, so the farmer will need to make a few trips to boat all three over to the other side. During the boating, he will always have to leave two things on their own on the banks of the river. For obvious reasons, the wolf cannot be left alone with the goat – he will devour it. The goat cannot be left with the cabbage, because she will eat it. How then, can the farmer transfer all three to the other side of the river, leaving them all intact?

Solution[edit]

The two solutions with the vertical axis denoting time, and brown, grey, green and beige paths denoting the wolf, goat, cabbage and boat, respectively

The first step that must be taken is to let the goat go across the river, as any other actions will result in the goat or the cabbage being eaten. When the farmer returns to the original side, he has the choice of taking either the wolf or the cabbage across next. If he takes the wolf across, he would have to return to get the cabbage, resulting in the wolf eating the goat. If he takes the cabbage across second, he will need to return to get the wolf, resulting in the cabbage being eaten by the goat. The dilemma is solved by taking the wolf (or the cabbage) over and bringing the goat back. Now he can take the cabbage (or the wolf) over, and finally return to fetch the goat.

An animation of the solution

His actions in the solution are summarized in the following steps:

1. Take the goat over
2. Return to other side
3. Take the wolf or cabbage over
4. Return with the goat
5. Take the cabbage or wolf over
6. Return
7. Take goat over

Thus there are seven crossings, four forward and three back.

Note: the key to the solution is realizing that one can bring things back (emphasized above). This is often unclear from the wording of the story, but never forbidden.

Source: https://www.futurelearn.com/info/courses/recreational-math/0/steps/43518
www,wikipedia