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River-crossing Problems
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 at the same time, or which or how many items may be safely left together.. The setting may vary cosmetically, for example, by replacing the river by a bridge. The earliest known river-crossing problems occur in the manuscript ''Propositiones ad Acuendos Juvenes'' ( en, Problems to sharpen the young), traditionally said to be written by Alcuin. The earliest copies of this manuscript date from the 9th century; it contains three river-crossing problems, including the fox, goose and bag of beans puzzle and the jealous husbands problem. Well-known river-crossing puzzles include: * The fox, goose and bag of beans puzzle, in which a farmer must transport a fox, goose and bag of beans from one side of a river to another using a boat which can ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Animation Of Cabbage, Sheep And Dog Crossing The River
Animation is a method by which image, still figures are manipulated to appear as Motion picture, moving images. In traditional animation, images are drawn or painted by hand on transparent cel, celluloid sheets to be photographed and exhibited on film. Today, most animations are made with computer-generated imagery (CGI). Computer animation can be very detailed Computer animation#Animation methods, 3D animation, while Traditional animation#Computers and traditional animation, 2D computer animation (which may have the look of traditional animation) can be used for stylistic reasons, low bandwidth, or faster real-time renderings. Other common animation methods apply a stop motion technique to two- and three-dimensional objects like cutout animation, paper cutouts, puppets, or Clay animation, clay figures. A cartoon is an animated film, usually a short film, featuring an cartoon, exaggerated visual style. The style takes inspiration from comic strips, often featuring anthropomorphi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stream Bed
A stream bed or streambed is the bottom of a stream or river (bathymetry) or the physical confine of the normal water flow (Channel (geography), channel). The lateral confines or channel margins are known as the stream Bank (geography), banks or river banks, during all but flood stage. Under certain conditions a river can branch from one stream bed to multiple stream beds. A flood occurs when a stream overflows its banks and flows onto its flood plain. As a general rule, the bed is the part of the stream channel, channel up to the normal water line, and the banks are that part above the normal water line. However, because water flow varies, this differentiation is subject to local interpretation. Usually, the bed is kept clear of terrestrial vegetation, whereas the banks are subjected to water flow only during unusual or perhaps infrequent high water stages and therefore might support vegetation some or much of the time. The nature of any stream bed is always a function of th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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. David Darling, ''The Internet Encyclopedia of Science''. Accessed on line February 7, 2008. The oldest known copy of the manuscript dates from the late 9th century. The text is attributed to Alcuin of York (died 804.) Some editions of the text contain 53 problems, others 56. It has been translated into English by John Hadley, with annotations by John Hadley and David Singmaster.Problems to Sharpen the Young John Hadley and David Singmaster, ''The Mathematical Gazette'', 76, #475 (Ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alcuin
Alcuin of York (; la, Flaccus Albinus Alcuinus; 735 – 19 May 804) – also called Ealhwine, Alhwin, or Alchoin – was a scholar, clergyman, poet, and teacher from York, Northumbria. He was born around 735 and became the student of Ecgbert of York, Archbishop Ecgbert at York. At the invitation of Charlemagne, he became a leading scholar and teacher at the Carolingian dynasty, Carolingian court, where he remained a figure in the 780s and 790s. Before that, he was also a court chancellor in Aachen. "The most learned man anywhere to be found", according to Einhard's ''Vita Karoli Magni, Life of Charlemagne'' (–833), he is considered among the most important intellectual architects of the Carolingian Renaissance. Among his pupils were many of the dominant intellectuals of the Carolingian era. During this period, he perfected Carolingian minuscule, an easily read manuscript hand using a mixture of upper- and lower-case letters. Latin paleography in the eighth centur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fox, Goose And Bag Of Beans Puzzle
The wolf, goat and cabbage problem is a river crossing puzzle. It dates back to at least the 9th century, and has entered the folklore of several cultures. The story A farmer with a wolf, a goat, and a cabbage 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jealous Husbands Problem
The missionaries and cannibals problem, and the closely related jealous husbands problem, are classic river-crossing problems, river-crossing logic puzzles. The missionaries and cannibals problem is a well-known toy problem in artificial intelligence, where it was used by Saul Amarel as an example of problem representation. The problem In the missionaries and cannibals problem, three missionaries and three cannibals must cross a river using a boat which can carry at most two people, under the constraint that, for both banks, if there are missionaries present on the bank, they cannot be outnumbered by cannibals (if they were, the cannibals would eat the missionaries). The boat cannot cross the river by itself with no people on board. And, in some variations, one of the cannibals has only one arm and cannot row. In the jealous husbands problem, the missionaries and cannibals become three married couples, with the constraint that no woman can be in the presence of another man unle ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wolf, Goat And Cabbage Problem
The wolf, goat and cabbage problem is a river crossing puzzle. It dates back to at least the 9th century, and has entered the folklore of several cultures. The story A farmer with a wolf, a goat, and a cabbage 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bridge And Torch Problem
The bridge and torch problem (also known as ''The Midnight Train'' and ''Dangerous crossing'') is a logic puzzle that deals with four people, a bridge and a torch. It is in the category of river crossing puzzles, where a number of objects must move across a river, with some constraints.Tricky Crossings , Ivars Peterson, ''Science News'', 164, #24 (December 13, 2003); accessed on line February 7, 2008. Story Four people come to a river in the night. There is a narrow bridge, and it can only hold two people at a time. They have one torch and, because it's night, the torch has to be used when crossing the bridge. Person A can cross the bridge in 1 minute, B in 2 minutes, C in 5 minutes, and D in 8 minutes. When two people cross the bridge together, they must move at the slower person's pace. The question is, c ...[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Timeline
A timeline is a display of a list of events in chronological order. It is typically a graphic design showing a long bar labelled with dates paralleling it, and usually contemporaneous events. Timelines can use any suitable scale representing time, suiting the subject and data; many use a linear scale, in which a unit of distance is equal to a set amount of time. This timescale is dependent on the events in the timeline. A timeline of evolution can be over millions of years, whereas a timeline for the day of the September 11 attacks can take place over minutes, and that of an explosion over milliseconds. While many timelines use a linear timescale—especially where very large or small timespans are relevant -- logarithmic timelines entail a logarithmic scale of time; some "hurry up and wait" chronologies are depicted with zoom lens metaphors. History Time and space, particularly the line, are intertwined concepts in human thought. The line is ubiquitous in clocks in the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wolf, Goat And Cabbage Problem
The wolf, goat and cabbage problem is a river crossing puzzle. It dates back to at least the 9th century, and has entered the folklore of several cultures. The story A farmer with a wolf, a goat, and a cabbage 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 by Saul Amarel as an example of problem representation. The problem In the missionaries and cannibals problem, three missionaries and three cannibals must cross a river using a boat which can carry at most two people, under the constraint that, for both banks, if there are missionaries present on the bank, they cannot be outnumbered by cannibals (if they were, the cannibals would eat the missionaries). The boat cannot cross the river by itself with no people on board. And, in some variations, one of the cannibals has only one arm and cannot row. In the jealous husbands problem, the missionaries and cannibals become three married couples, with the constraint that no woman can be in the presence of another man unless her husband is also ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graph-theoretic
In mathematics, graph theory is the study of ''graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') which are connected by '' edges'' (also called ''links'' or ''lines''). A distinction is made between undirected graphs, where edges link two vertices symmetrically, and directed graphs, where edges link two vertices asymmetrically. Graphs are one of the principal objects of study in discrete mathematics. Definitions Definitions in graph theory vary. The following are some of the more basic ways of defining graphs and related mathematical structures. Graph In one restricted but very common sense of the term, a graph is an ordered pair G=(V,E) comprising: * V, a set of vertices (also called nodes or points); * E \subseteq \, a set of edges (also called links or lines), which are unordered pairs of vertices (that is, an edge is associated with two ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
