The wolf, goat, and cabbage problem is a

river crossing puzzle A river crossing puzzle is a type of puzzle in which the object is to carry items from one river bank to another, usually in the fewest trips. The difficulty of the puzzle may arise from restrictions on which or how many items can be transported a ...

. It dates back to at least the 9th century, and has entered the

folklore Folklore is the body of expressive culture shared by a particular group of people, culture or subculture. This includes oral traditions such as Narrative, tales, myths, legends, proverbs, Poetry, poems, jokes, and other oral traditions. This also ...

of several cultures.

The story

A farmer with a

wolf The wolf (''Canis lupus''; : wolves), also known as the grey wolf or gray wolf, is a Canis, canine native to Eurasia and North America. More than thirty subspecies of Canis lupus, subspecies of ''Canis lupus'' have been recognized, includin ...

, a

goat The goat or domestic goat (''Capra hircus'') is a species of Caprinae, goat-antelope that is mostly kept as livestock. It was domesticated from the wild goat (''C. aegagrus'') of Southwest Asia and Eastern Europe. The goat is a member of the ...

, and a

cabbage Cabbage, comprising several cultivars of '' Brassica oleracea'', is a leafy green, red (purple), or white (pale green) biennial plant grown as an annual vegetable crop for its dense-leaved heads. It is descended from the wild cabbage ( ''B.& ...

must cross a river by boat. The boat can carry only the farmer and a single item. If left unattended together, the wolf would eat the goat, or the goat would eat the cabbage. How can they cross the river without anything being eaten?

Solution

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. 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 The nine dots puzzle is a mathematical puzzle whose task is to connect nine squarely arranged points with a pen by four (or fewer) straight lines without lifting the pen or retracing any lines. The puzzle has appeared under various other names ov ...

Occurrence and variations

The puzzle is one of a number of

s, where the object is to move a set of items across a river subject to various restrictions. In the earliest known occurrence of this problem, in the medieval manuscript ''

Propositiones ad Acuendos Juvenes The medieval Latin manuscript ''Propositiones ad Acuendos Juvenes'' () is one of the earliest known collections of recreational mathematics problems.''Alcuin's Transportation Problems and Integer Programming''
, Ralf Borndörfer, Martin Grötschel, and Andreas Löbel, preprint SC-95-27 (November 1995), Konrad-Zuse-Zentrum für Informationstechnik Berlin.^{, p. 26} fox, chicken, and grain; fox, goose and corn; and panther, pig, and porridge. 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. Another version of the puzzle stemming from a Chinese legend is recorded in an 18th-century painted panel by Japanese artist

Maruyama Ōkyo , born Maruyama Masataka, was a Japanese artist active in the late 18th century. He moved to Kyoto, during which he studied artworks from Chinese, Japanese and Western sources. A personal style of Western naturalism mixed with Eastern de ...

, in the collection of the British museum. 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. Following this legend, the subject of a tiger with her cubs became a traditional subject for art in east Asia. The depiction by Ōkyo shows the tiger family crossing a river, with the mother carrying one cub across the river at a time. 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 same variation of the puzzle has also been recorded as a

koan A ( ; ; zh, c=公案, p=gōng'àn ; ; ) is a story, dialogue, question, or statement from Chinese Chan Buddhist lore, supplemented with commentaries, that is used in Zen Buddhist practice in different ways. The main goal of practice in Z ...

Ryōan-ji Ryōan-ji (, , ''The Temple of the Dragon at Peace'') is a Zen temple located in northwest Kyoto, Japan. It belongs to the Myōshin-ji school of the Rinzai branch of Zen Buddhism. The Ryōan-ji garden is considered one of the finest surviving ex ...

, a

Zen Zen (; from Chinese: ''Chán''; in Korean: ''Sŏn'', and Vietnamese: ''Thiền'') is a Mahayana Buddhist tradition that developed in China during the Tang dynasty by blending Indian Mahayana Buddhism, particularly Yogacara and Madhyamaka phil ...

temple in

Kyoto Kyoto ( or ; Japanese language, Japanese: , ''Kyōto'' ), officially , is the capital city of Kyoto Prefecture in the Kansai region of Japan's largest and most populous island of Honshu. , the city had a population of 1.46 million, making it t ...

. The puzzle has been found in the folklore of African-Americans, Cameroon, the Cape Verde Islands, Denmark, Ethiopia, Ghana, Italy, Romania, Russia, Scotland, the Sudan, Uganda, Zambia, and Zimbabwe.^{, pp. 26–27;} It has been given the index number H506.3 in

Stith Thompson Stith Thompson (March 7, 1885 – January 10, 1976) was an American folklore studies, folklorist: he has been described as "America's most important folklorist". He is the "Thompson" of the Aarne–Thompson–Uther Index, which indexes Folklore, ...

's motif index of folk literature, and is ATU 1579 in the Aarne–Thompson classification system. The puzzle was a favorite of

Lewis Carroll Charles Lutwidge Dodgson (27 January 1832 – 14 January 1898), better known by his pen name Lewis Carroll, was an English author, poet, mathematician, photographer and reluctant Anglicanism, Anglican deacon. His most notable works are ''Alice ...

, and has been reprinted in various collections of

recreational mathematics Recreational mathematics is mathematics carried out for recreation (entertainment) rather than as a strictly research-and-application-based professional activity or as a part of a student's formal education. Although it is not necessarily limited ...

.^{, p. 26.} In his 'Arabian Nights' memoir, ''Meetings with Remarkable Men'', the metaphysical Magus,

G. I. Gurdjieff George Ivanovich Gurdjieff ( – 29 October 1949) was a philosopher, mystic, spiritual teacher, composer, and movements teacher. Born in the Russian Empire, he briefly became a citizen of the First Republic of Armenia after its formation in 19 ...

cites this riddle as "The Wolf, the goat and the cabbage". He notes, "This popular riddle clearly shows that...not solely by means of the ingenuity which every normal man should have, but that in addition he must not be lazy nor spare his strength, but must cross the river extra times for the attainment of his aim." Variations of the puzzle also appear in the adventure game '' Broken Sword: The Sleeping Dragon'', the

Nintendo DS The is a foldable handheld game console produced by Nintendo, released globally across 2004 and 2005. The DS, an initialism for "Developers' System" or "Dual Screen", introduced distinctive new features to handheld games: two LCD screens worki ...

puzzle game ''

Professor Layton and the Curious Village ''Professor Layton and the Curious Village'' is a puzzle video game, puzzle adventure game, adventure video game for the Nintendo DS system. It was developed and published by Level-5 (company), Level-5 in Japan and published by Nintendo worldwide. ...

'', and in ''

The Simpsons ''The Simpsons'' is an American animated sitcom created by Matt Groening and developed by Groening, James L. Brooks and Sam Simon for the Fox Broadcasting Company. It is a Satire (film and television), satirical depiction of American life ...

'' episode "

Gone Maggie Gone "Gone Maggie Gone" is the thirteenth episode of the twentieth season of the American animated television series ''The Simpsons''. It originally aired on the Fox network in the United States on March 15, 2009. The episode was written by both Bil ...

", where

Homer Homer (; , ; possibly born ) was an Ancient Greece, Ancient Greek poet who is credited as the author of the ''Iliad'' and the ''Odyssey'', two epic poems that are foundational works of ancient Greek literature. Despite doubts about his autho ...

has to get across a river with

Maggie Maggie or Maggy is a common short form of the name Magdalena, Magnolia, Margaret, or Marigold. People Maggie * Maggie Adamson, Scottish musician * Dame Maggie Aderin-Pocock (born 1968), British scientist * Maggie Alderson (born 1959), ...

Santa's Little Helper Santa's Little Helper is a fictional dog in the American animated television series ''The Simpsons''. He is the pet greyhound of the Simpson family. He was previously voiced by Frank Welker, and is currently voiced by Dan Castellaneta. The do ...

, and a jar of rat poison that looks like candy. In the ''

Class of 3000 ''Class of 3000'' is an American animated children's musical television series created by André 3000 (best known as a member of the hip hop duo Outkast) and Thomas W. Lynch for Cartoon Network. Produced by Tom Lynch Company and Moxie Turtle ...

'' episode "Westley Side Story", Sunny and his students perform a similar exercise involving a chicken, a

coyote The coyote (''Canis latrans''), also known as the American jackal, prairie wolf, or brush wolf, is a species of canis, canine native to North America. It is smaller than its close relative, the Wolf, gray wolf, and slightly smaller than the c ...

and a sack of corn. The ''

Between the Lions ''Between the Lions'' is an American animated/live-action/puppet educational children's television series designed to promote reading. The show is a co-production between WGBH in Boston, Sirius Thinking, Ltd., in New York City, and Mississipp ...

'' episode "Farmer Ken's Puzzle" portrays it being made into a computer game with a cat, a hen, and a sack of seeds. File:Playable_Fox_Chook_Corn_puzzle.svg, Interactive chicken, fox and grain problem. defaul

In the '' Bull (2016 TV series), Bull'' episode "Justice for Cable", Benny begins a riddle with "a man has a fox, a duck, and a bag of beans". Bull inexplicably declares "There is no answer", and everyone believes him. In some parts of Africa, variations on the puzzle have been found in which the boat can carry two objects instead of only one. When the puzzle is weakened in this way it is possible to introduce the extra constraint that no two items, including ''A'' and ''C'', can be left together.^{, p. 27.} In the '' Star Trek: Prodigy'' episode "Time Amok", a holographic version of

Kathryn Janeway Kathryn Janeway is a fictional character in the ''Star Trek'' franchise. She was the main character of the television series '' Star Trek: Voyager'', which aired between 1995 and 2001. She served as the captain of the Starfleet starship USS ''Vo ...

employs the tale (here told as the chicken, fox and grain problem) to teach the crew of the USS ''Protostar'' how to work together.

References

{{Reflist

External links

Goat, Cabbage and Wolf
A Javascript simulation
Fox, Chook and Corn
A simulation without Javascript needed Logic puzzles

The story

Solution

Occurrence and variations

See also

References

External links