Fox, goose and bag of beans puzzle
Encyclopedia
The fox, goose and bag of beans puzzle is a river-crossing puzzle. It dates back to at least the 9th century, and has entered the folklore
of a number of ethnic groups.
, a goose
, and a bag of beans. On his way home, the farmer came to the bank of a river and hired a boat. But in crossing the river by boat, the farmer could carry only himself and a single one of his purchases - the fox, the goose, or the bag of the beans.
If left alone, the fox would eat the goose, and the goose would eat the beans.
The farmer's challenge was to carry himself and his purchases to the far bank of the river, leaving each purchase intact. How did he do it?
His actions in the solution are summarised in the following steps:
Thus there are seven crossings, four forward and three back.
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 three objects are a wolf, a goat, and a cabbage. 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 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.
The puzzle has been found in the folklore
of African-Americans, Cameroon
, the Cape Verde Islands, Denmark
, Ethiopia
, Ghana
, Italy
, Russia
, Romania
, Scotland
, the Sudan
, Uganda
, Zambia
, and Zimbabwe
., pp. 26–27; It has been given the index number H506.3 in Stith Thompson
's motif index of folk literature, and is ATU 1579 in the Aarne-Thompson-Uther classification system.
The puzzle was a favorite of Lewis Carroll
, and has been reprinted in various collections of recreational mathematics
., p. 26.
A variation of the puzzle also appears in the Nintendo DS
puzzle game Professor Layton and the Curious Village
.
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.
Folklore
Folklore consists of legends, music, oral history, proverbs, jokes, popular beliefs, fairy tales and customs that are the traditions of a culture, subculture, or group. It is also the set of practices through which those expressive genres are shared. The study of folklore is sometimes called...
of a number of ethnic groups.
The story
Once upon a time a farmer went to market and purchased a foxFox
Fox is a common name for many species of omnivorous mammals belonging to the Canidae family. Foxes are small to medium-sized canids , characterized by possessing a long narrow snout, and a bushy tail .Members of about 37 species are referred to as foxes, of which only 12 species actually belong to...
, a goose
Goose
The word goose is the English name for a group of waterfowl, belonging to the family Anatidae. This family also includes swans, most of which are larger than true geese, and ducks, which are smaller....
, and a bag of beans. On his way home, the farmer came to the bank of a river and hired a boat. But in crossing the river by boat, the farmer could carry only himself and a single one of his purchases - the fox, the goose, or the bag of the beans.
If left alone, the fox would eat the goose, and the goose would eat the beans.
The farmer's challenge was to carry himself and his purchases to the far bank of the river, leaving each purchase intact. How did he do it?
Solution
The first step must be to bring the goose across the river, as any other will result in the goose or the beans being eaten. When the farmer returns to the original side, he has the choice of bringing either the fox or the beans across. If he brings the fox across, he must then return to bring the beans over, resulting in the fox eating the goose. If he brings the beans across, he will need to return to get the fox, resulting in the beans being eaten. Here he has a dilemma, solved by bringing the fox (or the beans) over and bringing the goose back. Now he can bring the beans (or the fox) over, leaving the goose, and finally return to fetch the goose.His actions in the solution are summarised in the following steps:
- Bring goose over
- Return
- Bring fox or beans over
- Bring goose back
- Bring beans or fox over
- Return
- Bring goose over
Thus there are seven crossings, four forward and three back.
Occurrence and variations
The puzzle is one of a number of river crossing puzzleRiver crossing puzzle
A river crossing puzzle is a type of transport puzzle in which the object is to carry items from one river bank to another. The difficulty of the puzzle may arise from restrictions on which or how many items can be transported at the same time, or from which or how many items may be safely left...
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
Propositiones ad Acuendos Juvenes
The medieval Latin manuscript Propositiones ad Acuendos Juvenes is one of the earliest known collections of recreational mathematics problems. The oldest known copy of the manuscript dates from the late 9th century. The text is attributed to Alcuin of York Some editions of the text contain 53...
, the three objects are a wolf, a goat, and a cabbage. 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 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.
The puzzle has been found in the folklore
Folklore
Folklore consists of legends, music, oral history, proverbs, jokes, popular beliefs, fairy tales and customs that are the traditions of a culture, subculture, or group. It is also the set of practices through which those expressive genres are shared. The study of folklore is sometimes called...
of African-Americans, Cameroon
Cameroon
Cameroon, officially the Republic of Cameroon , is a country in west Central Africa. It is bordered by Nigeria to the west; Chad to the northeast; the Central African Republic to the east; and Equatorial Guinea, Gabon, and the Republic of the Congo to the south. Cameroon's coastline lies on the...
, the Cape Verde Islands, Denmark
Denmark
Denmark is a Scandinavian country in Northern Europe. The countries of Denmark and Greenland, as well as the Faroe Islands, constitute the Kingdom of Denmark . It is the southernmost of the Nordic countries, southwest of Sweden and south of Norway, and bordered to the south by Germany. Denmark...
, Ethiopia
Ethiopia
Ethiopia , officially known as the Federal Democratic Republic of Ethiopia, is a country located in the Horn of Africa. It is the second-most populous nation in Africa, with over 82 million inhabitants, and the tenth-largest by area, occupying 1,100,000 km2...
, Ghana
Ghana
Ghana , officially the Republic of Ghana, is a country located in West Africa. It is bordered by Côte d'Ivoire to the west, Burkina Faso to the north, Togo to the east, and the Gulf of Guinea to the south...
, Italy
Italy
Italy , officially the Italian Republic languages]] under the European Charter for Regional or Minority Languages. In each of these, Italy's official name is as follows:;;;;;;;;), is a unitary parliamentary republic in South-Central Europe. To the north it borders France, Switzerland, Austria and...
, Russia
Russia
Russia or , officially known as both Russia and the Russian Federation , is a country in northern Eurasia. It is a federal semi-presidential republic, comprising 83 federal subjects...
, Romania
Romania
Romania is a country located at the crossroads of Central and Southeastern Europe, on the Lower Danube, within and outside the Carpathian arch, bordering on the Black Sea...
, Scotland
Scotland
Scotland is a country that is part of the United Kingdom. Occupying the northern third of the island of Great Britain, it shares a border with England to the south and is bounded by the North Sea to the east, the Atlantic Ocean to the north and west, and the North Channel and Irish Sea to the...
, the Sudan
Sudan
Sudan , officially the Republic of the Sudan , is a country in North Africa, sometimes considered part of the Middle East politically. It is bordered by Egypt to the north, the Red Sea to the northeast, Eritrea and Ethiopia to the east, South Sudan to the south, the Central African Republic to the...
, Uganda
Uganda
Uganda , officially the Republic of Uganda, is a landlocked country in East Africa. Uganda is also known as the "Pearl of Africa". It is bordered on the east by Kenya, on the north by South Sudan, on the west by the Democratic Republic of the Congo, on the southwest by Rwanda, and on the south by...
, Zambia
Zambia
Zambia , officially the Republic of Zambia, is a landlocked country in Southern Africa. The neighbouring countries are the Democratic Republic of the Congo to the north, Tanzania to the north-east, Malawi to the east, Mozambique, Zimbabwe, Botswana and Namibia to the south, and Angola to the west....
, and Zimbabwe
Zimbabwe
Zimbabwe is a landlocked country located in the southern part of the African continent, between the Zambezi and Limpopo rivers. It is bordered by South Africa to the south, Botswana to the southwest, Zambia and a tip of Namibia to the northwest and Mozambique to the east. Zimbabwe has three...
., pp. 26–27; It has been given the index number H506.3 in Stith Thompson
Stith Thompson
Stith Thompson was an American scholar of folklore. He is the "Thompson" of the Aarne-Thompson classification system.- Biography :...
's motif index of folk literature, and is ATU 1579 in the Aarne-Thompson-Uther classification system.
The puzzle was a favorite of Lewis Carroll
Lewis Carroll
Charles Lutwidge Dodgson , better known by the pseudonym Lewis Carroll , was an English author, mathematician, logician, Anglican deacon and photographer. His most famous writings are Alice's Adventures in Wonderland and its sequel Through the Looking-Glass, as well as the poems "The Hunting of the...
, and has been reprinted in various collections of recreational mathematics
Recreational mathematics
Recreational mathematics is an umbrella term, referring to mathematical puzzles and mathematical games.Not all problems in this field require a knowledge of advanced mathematics, and thus, recreational mathematics often attracts the curiosity of non-mathematicians, and inspires their further study...
., p. 26.
A variation of the puzzle also appears in the Nintendo DS
Nintendo DS
The is a portable game console produced by Nintendo, first released on November 21, 2004. A distinctive feature of the system is the presence of two separate LCD screens, the lower of which is a touchscreen, encompassed within a clamshell design, similar to the Game Boy Advance SP...
puzzle game Professor Layton and the Curious Village
Professor Layton and the Curious Village
Professor Layton and the Curious Village, released in Japan as , is a puzzle adventure video game for the Nintendo DS system. It was developed by Level-5, and published by Level-5 within Japan and Nintendo internationally. It was released in Japan during 2007, and in PAL regions and North America a...
.
In some parts of Africa
Africa
Africa is the world's second largest and second most populous continent, after Asia. At about 30.2 million km² including adjacent islands, it covers 6% of the Earth's total surface area and 20.4% of the total land area...
, 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.
External links
- Goat, Cabbage and Wolf A Java simulation