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List Of Impossible Puzzles
This is a list of puzzles that cannot be solved. An impossible puzzle is a puzzle that cannot be resolved, either due to lack of sufficient information, or any number of logical impossibilities. * 15 puzzle – Slide fifteen numbered tiles into numerical order. Impossible for half of the starting positions. * Five room puzzle – Cross each wall of a diagram exactly once with a continuous line. * MU puzzle – Transform the string to according to a set of rules. * Mutilated chessboard problem – Place 31 dominoes of size 2×1 on a chessboard with two opposite corners removed. * Coloring the edges of the Petersen graph with three colors. * Seven Bridges of Königsberg – Walk through a city while crossing each of seven bridges exactly once. * Three cups problem – Turn three cups right-side up after starting with one wrong and turning two at a time. * Three utilities problem – Connect three cottages to gas, water, and electricity without crossing lines. * Thirty-six offi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Puzzle
A puzzle is a game, Problem solving, problem, or toy that tests a person's ingenuity or knowledge. In a puzzle, the solver is expected to put pieces together (Disentanglement puzzle, or take them apart) in a logical way, in order to arrive at the correct or fun solution of the puzzle. There are different genres of puzzles, such as crossword puzzles, word-search puzzles, number puzzles, relational puzzles, and logic puzzles. The academic study of puzzles is called enigmatology. Puzzles are often created to be a form of entertainment but they can also arise from serious Mathematical problem, mathematical or logical problems. In such cases, their solution may be a significant contribution to mathematical research. Etymology The ''Oxford English Dictionary'' dates the word ''puzzle'' (as a verb) to the end of the 16th century. Its earliest use documented in the ''OED'' was in a book titled ''The Voyage of Robert Dudley (explorer), Robert Dudley...to the West Indies, 1594–95, narra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Three Utilities Problem
The classical mathematical puzzle known as the three utilities problem or sometimes water, gas and electricity asks for non-crossing connections to be drawn between three houses and three utility companies in the plane. When posing it in the early 20th century, Henry Dudeney wrote that it was already an old problem. It is an impossible puzzle: it is not possible to connect all nine lines without crossing. Versions of the problem on nonplanar surfaces such as a torus or Möbius strip, or that allow connections to pass through other houses or utilities, can be solved. This puzzle can be formalized as a problem in topological graph theory by asking whether the complete bipartite graph K_, with vertices representing the houses and utilities and edges representing their connections, has a graph embedding in the plane. The impossibility of the puzzle corresponds to the fact that K_ is not a planar graph. Multiple proofs of this impossibility are known, and form part of the proof of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unsolvable Puzzles
"Unsolvable" is the twenty-first episode of the first season of the American television police sitcom series ''Brooklyn Nine-Nine''. Written by co-executive producer Prentice Penny and directed by Ken Whittingham, it aired on Fox in the United States on March 18, 2014. In this episode, Jake decides to take on an 8-year-old case that is deemed "unsolvable" and seeks Terry's help in solving it; Amy, planning a romantic vacation with her boyfriend Teddy, tries to obscure her true intentions from Holt; and Boyle, downcast after the end of his relationship, is told of a great secret. The episode was seen by an estimated 2.50 million household viewers and gained a 1.1/3 ratings share among adults aged 18–49, according to Nielsen Media Research. The episode received mostly positive reviews from critics, who praised Andy Samberg's performance. Plot When Jake is allowed the weekend off because of a hot streak in solving cases, he decides to take on an 8-year old cold case that everyon ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Undecidable Problems
In computability theory, an undecidable problem is a type of computational problem that requires a yes/no answer, but where there cannot possibly be any computer program that always gives the correct answer; that is, any possible program would sometimes give the wrong answer or run forever without giving any answer. More formally, an undecidable problem is a problem whose language is not a recursive set; see the article Decidable language. There are uncountably many undecidable problems, so the list below is necessarily incomplete. Though undecidable languages are not recursive languages, they may be subsets of Turing recognizable languages: i.e., such undecidable languages may be recursively enumerable. Many, if not most, undecidable problems in mathematics can be posed as word problems: determining when two distinct strings of symbols (encoding some mathematical concept or object) represent the same object or not. For undecidability in axiomatic mathematics, see List of stateme ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Word Puzzle
Word games (also called word game puzzles or word search games) are spoken, board, or video games often designed to test ability with language or to explore its properties. Word games are generally used as a source of entertainment, but can additionally serve an educational purpose. Young children can enjoy playing games such as Hangman, while naturally developing important language skills like spelling. Researchers have found that adults who regularly solved crossword puzzles, which require familiarity with a larger vocabulary, had better brain function later in life. Popular word-based game shows have been a part of television and radio throughout broadcast history, including '' Spelling Bee'', the first televised game show, and ''Wheel of Fortune'', the longest-running syndicated game show in the United States. Categories of word game Letter arrangement games In a letter arrangement game, the goal is to form words out of given letters. These games generally test vocab ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
-gry Puzzle
The ''-gry'' puzzle is a popular word puzzle that asks for the third English word that ends with the letters ''-gry'' other than ''angry'' and ''hungry''. Specific wording varies substantially, but the puzzle has no clear answer, as there are no other common English words that end in ''-gry''. Interpretations of the puzzle suggest it is either an answerless hoax; a trick question; a sincere question asking for an obscure word; or a corruption of a more straightforward puzzle, which may have asked for words containing ''gry'' (such as ''gryphon''). Of these, countless trick question variants and obscure English words (or nonce words) have been proposed. The lack of a conclusive answer has ensured the enduring popularity of the puzzle, and it has become one of the most frequently asked word puzzles. The ultimate origin and original form of the puzzle is unknown, but it was popularized in 1975, starting in the New York area, and has remained popular into the 21st century. Various si ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Impossible Puzzle
The Sum and Product Puzzle, also known as the Impossible Puzzle because it seems to lack sufficient information for a solution, is a logic puzzle. It was first published in 1969 by Hans Freudenthal, and the name ''Impossible Puzzle'' was coined by Martin Gardner.. The puzzle is solvable, though not easily. There exist many similar puzzles. Puzzle ''X'' and ''Y'' are two different whole numbers greater than 1. Their sum is not greater than 100. S and P are two mathematicians (and consequently perfect logicians); S knows the sum ''X'' + ''Y'' and P knows the product ''X'' × ''Y''. Both S and P know all the information in this paragraph. In following conversation, both participants are always telling the truth: *S says "P does not know ''X'' and ''Y''." *P says "Now I know ''X'' and ''Y''." *S says "Now I also know ''X'' and ''Y''." What are ''X'' and ''Y''? Explanation The problem is rather easily solved once the concepts and perspectives are made clear. There are three partie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thirty-six Officers Problem
In combinatorics, two Latin squares of the same size (''order'') are said to be ''orthogonal'' if when superimposed the ordered paired entries in the positions are all distinct. A set of Latin squares, all of the same order, all pairs of which are orthogonal is called a set of mutually orthogonal Latin squares. This concept of orthogonality in combinatorics is strongly related to the concept of blocking in statistics, which ensures that independent variables are truly independent with no hidden confounding correlations. "Orthogonal" is thus synonymous with "independent" in that knowing one variable's value gives no further information about another variable's likely value. An outdated term for pair of orthogonal Latin squares is ''Graeco-Latin square'', found in older literature. Graeco-Latin squares A Graeco-Latin square or Euler square or pair of orthogonal Latin squares of order over two sets and (which may be the same), each consisting of symbols, is an arrangement of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Three Cups Problem
The three cups problem, also known as the three cup challenge and other variants, is a mathematical puzzle that, in its most common form, cannot be solved. In the beginning position of the problem, one cup is upside-down and the other two are right-side up. The objective is to ''turn all cups right-side up'' in no more than six moves, turning over exactly two cups at each move. The solvable (but trivial) version of this puzzle begins with one cup right-side up and two cups upside-down. To solve the puzzle in a single move, turn up the two cups that are upside down — after which all three cups are facing up. As a magic trick, a magician can perform the solvable version in a convoluted way, and then ask an audience member to solve the unsolvable version. Proof of impossibility To see that the problem is insolvable (when starting with just one cup upside down), it suffices to concentrate on the number of cups the wrong way up. Denoting this number by W, the goal of the problem is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logical
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises in a topic-neutral way. When used as a countable noun, the term "a logic" refers to a logical formal system that articulates a proof system. Formal logic contrasts with informal logic, which is associated with informal fallacies, critical thinking, and argumentation theory. While there is no general agreement on how formal and informal logic are to be distinguished, one prominent approach associates their difference with whether the studied arguments are expressed in formal or informal languages. Logic plays a central role in multiple fields, such as philosophy, mathematics, computer science, and linguistics. Logic studies arguments, which consist of a set of premises together with a conclusion. Premises and conclusions are usually und ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Seven Bridges Of Königsberg
The Seven Bridges of Königsberg is a historically notable problem in mathematics. Its negative resolution by Leonhard Euler in 1736 laid the foundations of graph theory and prefigured the idea of topology. The city of Königsberg in Prussia (now Kaliningrad, Russia) was set on both sides of the Pregel River, and included two large islands—Kneiphof and Lomse—which were connected to each other, and to the two mainland portions of the city, by seven bridges. The problem was to devise a walk through the city that would cross each of those bridges once and only once. By way of specifying the logical task unambiguously, solutions involving either # reaching an island or mainland bank other than via one of the bridges, or # accessing any bridge without crossing to its other end are explicitly unacceptable. Euler proved that the problem has no solution. The difficulty he faced was the development of a suitable technique of analysis, and of subsequent tests that established this ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Petersen Graph
In the mathematical field of graph theory, the Petersen graph is an undirected graph with 10 vertices and 15 edges. It is a small graph that serves as a useful example and counterexample for many problems in graph theory. The Petersen graph is named after Julius Petersen, who in 1898 constructed it to be the smallest bridgeless cubic graph with no three-edge-coloring. Although the graph is generally credited to Petersen, it had in fact first appeared 12 years earlier, in a paper by . Kempe observed that its vertices can represent the ten lines of the Desargues configuration, and its edges represent pairs of lines that do not meet at one of the ten points of the configuration. Donald Knuth states that the Petersen graph is "a remarkable configuration that serves as a counterexample to many optimistic predictions about what might be true for graphs in general." The Petersen graph also makes an appearance in tropical geometry. The cone over the Petersen graph is naturally identif ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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