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The wolf, goat and cabbage problem is a
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 
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 shared by a particular group of people; it encompasses the traditions common to that culture, subculture or group. This includes oral traditions such as tales, legends, proverbs and jokes. They include material culture, ranging ...
of several cultures.
The story
A farmer with awolf
The wolf (''Canis lupus''; : wolves), also known as the gray wolf or grey wolf, is a large canine native to Eurasia and North America. More than thirty subspecies of ''Canis lupus'' have been recognized, and gray wolves, as popularly u ...
, a goat
The goat or domestic goat (''Capra hircus'') is a domesticated species of goat-antelope typically 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 a ...
, 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.&nb ...
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.
The puzzle has appeared under various other names over the years.
History ...
.
Occurrence and variations
The puzzle is one of a number ofriver 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 ...
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 language, Latin manuscript ''Propositiones ad Acuendos Juvenes'' ( en, Problems to Sharpen the Young) is one of the earliest known collections of recreational mathematics problems.''Alcuin's Transportation Problems and Integer Programming''
, Ralf Borndörfer,
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
Goat, Cabbage and Wolf
A Javascript simulation
Fox, Chook and Corn
A simulation without Javascript needed Logic puzzles
, Ralf Borndörfer,
Martin Grötschel
Martin Grötschel (born 10 September 1948) is a German mathematician known for his research on combinatorial optimization, polyhedral combinatorics, and operations research. From 1991 to 2012 he was Vice President of the Zuse Institute Berlin ( ...
, 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 deco ...
, 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 (; , ; ko, 화두, ; vi, công án) is a story, dialogue, question, or statement which is used in Zen practice to provoke the "great doubt" and to practice or test a student's progress in Zen.
Etymology
The Japanese term is the Sino-Jap ...
of Ryōan-ji
Ryōan-ji ( ja, 竜安寺, label=Shinjitai, ja, 龍安寺, label=Kyūjitai, ''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 ...
, a Zen
Zen ( zh, t=禪, p=Chán; ja, text= 禅, translit=zen; ko, text=선, translit=Seon; vi, text=Thiền) is a school of Mahayana Buddhism that originated in China during the Tang dynasty, known as the Chan School (''Chánzong'' 禪宗), and ...
temple in Kyoto
Kyoto (; Japanese: , ''Kyōto'' ), officially , is the capital city of Kyoto Prefecture in Japan. Located in the Kansai region on the island of Honshu, Kyoto forms a part of the Keihanshin metropolitan area along with Osaka and Kobe. , the ci ...
.
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 folklorist: he has been described as "America's most important folklorist".
He is the "Thompson" of the Aarne–Thompson–Uther Index, which indexes folktales by type, and the ...
'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 and mathematician. His most notable works are ''Alice's Adventures in Wonderland'' (1865) and its sequel ...
, 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 (; rus, Гео́ргий Ива́нович Гурджи́ев, r=Geórgy Ivánovich Gurdzhíev, p=ɡʲɪˈorɡʲɪj ɪˈvanəvʲɪd͡ʑ ɡʊrd͡ʐˈʐɨ(j)ɪf; hy, Գեորգի Իվանովիչ Գյուրջիև; c. 1 ...
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 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 working in tan ...
puzzle game ''Professor Layton and the Curious Village
''Professor Layton and the Curious Village'' is a puzzle adventure video game for the Nintendo DS system. It was developed by Level-5 and published by Level-5 in Japan and Nintendo worldwide. It was released in Japan in 2007 and worldwide the fol ...
'', and in ''The Simpsons
''The Simpsons'' is an American animated sitcom created by Matt Groening for the Fox Broadcasting Company. The series is a satirical depiction of American life, epitomized by the Simpson family, which consists of Homer, Marge, Bart, Lisa, ...
'' 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 Billy ...
", where Homer
Homer (; grc, Ὅμηρος , ''Hómēros'') (born ) was a 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. Homer is considered one of the ...
has to get across a river with Maggie
Maggie is a common short form of the name Magdalena, Magnolia, Margaret.
Maggie may refer to:
People
Women
* Maggie Adamson, Scottish musician
* Maggie Aderin-Pocock (born 1968), British scientist
* Maggie Alderson (born 1959), Aust ...
, 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 dog ...
, and a jar of rat poison that looks like candy. In the ''Class of 3000
''Class of 3000'' is an American animated musical television series created by André 3000 (best known as a member of the hip hop duo Outkast) for Cartoon Network. The series follows superstar and music teacher Sunny Bridges (voiced by 3000), ...
'' episode "Westley Side Story", Sunny and his students perform a similar exercise involving a chicken, a coyote
The coyote (''Canis latrans'') is a species of canis, canine native to North America. It is smaller than its close relative, the wolf, and slightly smaller than the closely related eastern wolf and red wolf. It fills much of the same ecologica ...
and a sack of corn. The ''Between the Lions
''Between the Lions'' is an American animated/live-action/puppet children's television series designed to promote reading. The show was a co-production between WGBH in Boston and Sirius Thinking, Ltd., in New York City, in association with Miss ...
'' episode "Farmer Ken's Puzzle" portrays it being made into a computer game with a cat, a hen, and a sack of seeds.
Kathryn Janeway
Kathryn Janeway is a fictional character in the ''Star Trek'' franchise. She was the Captain of the Starfleet starship USS ''Voyager'' (on '' Star Trek: Voyager'') while it was lost in the Delta Quadrant on the other side of the galaxy. After re ...
employs the tale (here told as the chicken, fox and grain problem) to teach the crew of the USS ''Protostar'' how to work together.
See also
*Missionaries and cannibals problem
The missionaries and cannibals problem, and the closely related jealous husbands problem, are classic river-crossing logic puzzles. The missionaries and cannibals problem is a well-known toy problem in artificial intelligence, where it was used b ...
References
{{ReflistExternal links
Goat, Cabbage and Wolf
A Javascript simulation
Fox, Chook and Corn
A simulation without Javascript needed Logic puzzles