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Impossible Puzzle
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. It is impossible to solve in 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. * Squaring the circle, the impossible problem of constructing a square with the same area as a given circle, using only a compass and straightedge. * Three cups problem – Turn three cups right-side up after starting with one ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Thirty-six Officers Problem
36 (thirty-six) is the natural number following 35 and preceding 37. In mathematics 36 is both the square of six, and the eighth triangular number or the sum of the first eight non-zero positive integers, which makes 36 the first non-trivial square triangular number. Aside from being the smallest square triangular number other than 1, it is also the only triangular number (other than 1) whose square root is also a triangular number. 36 is also the eighth refactorable number, as it has exactly nine positive divisors, and 9 is one of them; in fact, it is the smallest positive integer with at least nine divisors, which leads 36 to be the 7th highly composite number. It is the sum of the fourth pair of twin-primes ( 17 + 19), and the 18th Harshad number in decimal, as it is divisible by the sum of its digits (9). It is the smallest number n with exactly eight solutions ( 37, 57, 63, 74, 76, 108, 114, 126) to the Euler totient function \phi(x)=n. Adding up some subsets of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Puzzle
A puzzle is a game, problem, or toy that tests a person's ingenuity or knowledge. In a puzzle, the solver is expected to put pieces together ( or take them apart) in a logical way, in order to find the 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 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 16th century. Its earliest use documented in the ''OED'' was in a book titled ''The Voyage of Robert Dudley...to the West Indies, 1594–95, narrated by Capt. Wyatt, by himself, and by Abram Kendall, master'' (published circa 1595). The word later came to be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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 i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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 In the cold open, the squad notices Holt's injured his wrist and speculate what could have led to it. Holt breaks them up and secretl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
List Of Undecidable Problems
In computability theory, an undecidable problem is a decision problem for which an effective method (algorithm) to derive the correct answer does not exist. 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 statements undecidable in ZFC. Problems about abstract machines * The halting problem (determining whether a Turing machine halts on a given input) and the morta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Word Puzzle
Word games are spoken, board, card 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 may enjoy playing games such as Mad Libs Junior, while developing spelling and writing skills. 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 Letter arrangement games In a letter arrangement game, the goal is to form words out of given letters. These games generally test vocabulary skills as well as lateral thinking skills. Some examples of letter ar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
-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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Impossible Puzzle
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. It is impossible to solve in 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. * Squaring the circle, the impossible problem of constructing a square with the same area as a given circle, using only a compass and straightedge. * Three cups problem – Turn three cups right-side up after starting with one ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Three Utilities Problem
The three utilities problem, also known as water, gas and electricity, is a mathematical puzzle that asks for non-crossing connections to be drawn between three houses and three utility companies on a Plane (geometry), plane. When posing it in the early 20th century, Henry Dudeney wrote that it was already an old problem. It is an List of impossible puzzles, impossible puzzle: it is not possible to connect all nine lines without any of them 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 impossibili ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Compass And Straightedge
In geometry, straightedge-and-compass construction – also known as ruler-and-compass construction, Euclidean construction, or classical construction – is the construction of lengths, angles, and other geometric figures using only an Idealization (science philosophy), idealized ruler and a Compass (drawing tool), compass. The idealized ruler, known as a straightedge, is assumed to be infinite in length, have only one edge, and no markings on it. The compass is assumed to have no maximum or minimum radius, and is assumed to "collapse" when lifted from the page, so it may not be directly used to transfer distances. (This is an unimportant restriction since, using a multi-step procedure, a distance can be transferred even with a collapsing compass; see compass equivalence theorem. Note however that whilst a non-collapsing compass held against a straightedge might seem to be equivalent to marking it, the neusis construction is still impermissible and this is what unmarked really ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Logical
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure of arguments alone, independent of their topic and content. Informal logic is associated with informal fallacies, critical thinking, and argumentation theory. Informal logic examines arguments expressed in natural language whereas formal logic uses formal language. When used as a countable noun, the term "a logic" refers to a specific logical formal system that articulates a proof system. Logic plays a central role in many fields, such as philosophy, mathematics, computer science, and linguistics. Logic studies arguments, which consist of a set of premises that leads to a conclusion. An example is the argument from the premises "it's Sunday" and "if it's Sunday then I don't have to work" leading to the conclusion "I don't have to work." Premi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Squaring The Circle
Squaring the circle is a problem in geometry first proposed in Greek mathematics. It is the challenge of constructing a square (geometry), square with the area of a circle, area of a given circle by using only a finite number of steps with a compass and straightedge. The difficulty of the problem raised the question of whether specified axioms of Euclidean geometry concerning the existence of Line (geometry), lines and circles implied the existence of such a square. In 1882, the task was proven to be impossible, as a consequence of the Lindemann–Weierstrass theorem, which proves that pi (\pi) is a transcendental number. That is, \pi is not the zero of a function, root of any polynomial with Rational number, rational coefficients. It had been known for decades that the construction would be impossible if \pi were transcendental, but that fact was not proven until 1882. Approximate constructions with any given non-perfect accuracy exist, and many such constructions have been f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
