Editing Wolf, goat and cabbage problem (section)

==Solution==

[[File:fox_goose_beans_puzzle_solution.svg|thumb|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. 

[[File:Animasi untuk musang, angsa dan kekacang teka teki.png|thumb|An animation of the solution]]
His actions in the solution are summarized in the following steps:

# Take the goat over
# Return empty-handed
# Take the wolf or cabbage over
# Return with the goat
# Take whichever wasn't taken in step 3 over
# Return empty-handed
# Take the goat over

There are seven crossings: four forward and three back.

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. Knowing this will make the problem easy to solve even by small children. The focus of the puzzle is not just task scheduling, but creative thinking, similarly to the [[Nine dots puzzle]].

[[File:Fox_goose_beans_puzzle_visualisation.svg|thumb|Visualisation of the moves possible in the puzzle. Uppercase letters denote the Fox, Goose and Beans at the destination, and lowercase ones denote them at the origin. Movement of each object is represented by a coordinate axis. All the 8 valid and invalid placements are shown as vertices of a cube, and all 12 movements as its edges. Invalid moves are crossed out, leaving the 2 solutions shown in blue and purple.]]