The same variation of the puzzle has also been recorded as a koan of Ryōan-ji, a Zen temple in Kyoto. This depicts a puzzle equivalent to the puzzle of the wolf, goat, and cabbage, asking how the mother can do this without leaving the leopard cub alone with any of the other tiger cubs. The depiction by Ōkyo shows the tiger family crossing a river, with the mother carrying one cub across the river at a time. Following this legend, the subject of a tiger with her cubs became a traditional subject for art in east Asia. According to the legend, when a tiger has three cubs, one of them will be a leopard rather than a tiger, and more fierce than the others. The logic of the puzzle, in which there are three objects, A, B, and C, such that neither A and B nor B and C can be left together, remains the same.Īnother version of the puzzle stemming from a Chinese legend is recorded in an 18th-century painted panel by Japanese artist Maruyama Ōkyo, in the collection of the British museum. In the earliest known occurrence of this problem, in the medieval manuscript Propositiones ad Acuendos Juvenes, the three objects are a wolf, a goat, and a cabbage, but other cosmetic variations of the puzzle also exist, such as: wolf, sheep, and cabbage, p. 26 fox, chicken, and grain fox, goose and corn and panther, pig, and porridge. The puzzle is one of a number of river crossing puzzles, where the object is to move a set of items across a river subject to various restrictions. Invalid moves are crossed out, leaving the 2 solutions shown in blue and purple. All the 8 valid and invalid placements are shown as vertices of a cube, and all 12 movements as its edges. Movement of each object is represented by a coordinate axis. Uppercase letters denote the Fox, Goose and Beans at the destination, and lowercase ones denote them at the origin. Visualisation of the moves possible in the puzzle. The focus of the puzzle is not just task scheduling, but creative thinking, similarly to the Nine dots puzzle. Knowing this will make the problem easy to solve even by small children. This is often unclear from the wording of the story, but never forbidden. The key to the solution is realizing that one can bring things back (emphasized above). There are seven crossings: four forward and three back. Take whichever wasn't taken in step 3 over.His actions in the solution are summarized in the following steps: Now he can take the cabbage (or the wolf) over, and finally return to fetch the goat. The dilemma is solved by taking the wolf (or the cabbage) over and bringing the goat back. 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. If he takes the wolf across, he would have to return to get the cabbage, resulting in the wolf eating the goat. When the farmer returns to the original side, he has the choice of taking either the wolf or the cabbage across next. 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. Solution The two solutions with the vertical axis denoting time, and brown, grey, green and beige paths denoting the wolf, goat, cabbage and boat, respectively How can they cross the river without anything being eaten? If left unattended together, the wolf would eat the goat, or the goat would eat the cabbage. The boat can carry only the farmer and a single item. The story Ī farmer with a wolf, a goat, and a cabbage must cross a river by boat. It dates back to at least the 9th century, and has entered the folklore of several cultures. The wolf, goat and cabbage problem is a river crossing puzzle. River crossing puzzle Illuminated illustration depicting the wolf, goat and cabbage problem in the Ormesby Psalter, dating to 1250–1330
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