A dissection puzzle called a transformation puzzle or Richter Puzzle, is a tiling puzzle where a set of pieces can be assembled in different ways to produce two or more distinct geometric shapes. The creation of new dissection puzzles is considered to be a type of dissection puzzle. Puzzles may include various restraints, such as hinged pieces, pieces that can fold, or pieces that can twist. Creators of new dissection puzzles emphasize using a minimum number of pieces, or creating novel situations, such as ensuring that every piece connects to another with a hinge. Dissection puzzles are an early form of geometric puzzle; the earliest known descriptions of dissection puzzles are from the time of Plato in Ancient Greece, involve the challenge of turning two equal squares into one larger square using four pieces. Other ancient dissection puzzles were used as graphic depictions of the Pythagorean theorem. A famous ancient Greek dissection puzzle is the Ostomachion, a mathematical treatise attributed to Archimedes.
In the 10th century, Arabic mathematicians used geometric dissections in their commentaries on Euclid's Elements. In the 18th century, Chinese scholar Tai Chen described an elegant dissection for approximating the value of π; the puzzles saw a major increase in general popularity in the late 19th century when newspapers and magazines began running dissection puzzles. Puzzle creators Sam Loyd in the United States and Henry Dudeney in the United Kingdom were among the most published. Since dissection puzzles have been used for entertainment and maths education, creation of complex dissection puzzles is considered an exercise of geometric principles by mathematicians and math students; the dissections of regular polygons and other simple geometric shapes into another such shape was the subject of Martin Gardner's November 1961 "Mathematical Games column" in Scientific American. The haberdasher's problem shown in the figure below shows how to divide up a square and rearrange the pieces to make an equilateral triangle.
The column included a table of such best known dissections involving the square, hexagon, greek cross, so on. Some types of dissection puzzle are intended to create a large number of different geometric shapes; the tangram is a popular dissection puzzle of this type. The seven pieces can be configured into one of a few home shapes, such as the large square and rectangle that the pieces are stored in, to any number of smaller squares, parallelograms, or esoteric shapes and figures; some geometric forms are easy to create. This variability has ensured the puzzle's popularity. Other dissections are intended to move between a pair of geometric shapes, such as a triangle to a square, or a square to a five-pointed star. A dissection puzzle of this description is the haberdasher's problem, proposed in 1907 by Henry Dudeney; the puzzle is a dissection of a triangle to a square, in only four pieces. It is one of the simplest regular polygon to square dissections known, is now a classic example, it is not known whether a dissection of an equilateral triangle to a square is possible with three pieces.
Ostomachion Pizza theorem Puzzle Coffin, Stewart T.. The Puzzling World of Polyhedral Dissections. Oxford University Press. ISBN 0-19-853207-5. Frederickson, Greg N.. Dissections: Plane and Fancy. Cambridge University Press. ISBN 0-521-57197-9. Frederickson, Greg N.. Hinged Dissections: Swinging and Twisting. Cambridge University Press. ISBN 0-521-81192-9. Frederickson, Greg N.. Piano-hinged Dissections: Time to Fold!. A K Peters. ISBN 1-56881-299-X. Weisstein, Eric W.. "Haberdasher's Problem". MathWorld. Wolfram Web Resources. Retrieved 2006-08-08
A sliding puzzle, sliding block puzzle, or sliding tile puzzle is a combination puzzle that challenges a player to slide pieces along certain routes to establish a certain end-configuration. The pieces to be moved may consist of simple shapes, or they may be imprinted with colors, sections of a larger picture, numbers, or letters. Sliding puzzles are two-dimensional in nature if the sliding is facilitated by mechanically interlinked pieces or three-dimensional tokens; as this example shows, some sliding puzzles are mechanical puzzles. However, the mechanical fixtures are not essential to these puzzles. Unlike other tour puzzles, a sliding block puzzle prohibits lifting any piece off the board; this property separates sliding puzzles from rearrangement puzzles. Hence, finding moves and the paths opened up by each move within the two-dimensional confines of the board are important parts of solving sliding block puzzles; the oldest type of sliding puzzle is the fifteen puzzle, invented by Noyes Chapman in 1880.
Chapman's invention initiated a puzzle craze in the early 1880s. From the 1950s through the 1980s sliding puzzles employing letters to form words were popular; these sorts of puzzles have several possible solutions, as may be seen from examples such as Ro-Let, Scribe-o, Lingo. The fifteen puzzle has been computerized and examples are available to play for free on-line from many Web pages, it is a descendant of the jigsaw puzzle. The last square of the puzzle is displayed automatically once the other pieces have been lined up. Fifteen puzzle Klotski Minus Cube Rush Hour Sokoban Puzzle Mechanical puzzle Combination puzzle Rubik's Cube Ro – A rotational variation Sliding Piece Puzzles is said to be the definitive volume on this type of puzzle. Winning Ways The 15 Puzzle US Patent 4872682 - sliding puzzle wrapped on Rubik's Cube
A maze is a path or collection of paths from an entrance to a goal. The word is used to refer both to branching tour puzzles through which the solver must find a route, to simpler non-branching patterns that lead unambiguously through a convoluted layout to a goal; the pathways and walls in a maze are fixed, but puzzles in which the walls and paths can change during the game are categorised as mazes or tour puzzles. Mazes have been built with walls and rooms, with hedges, corn stalks, hay bales, paving stones of contrasting colors or designs, brick, or in fields of crops such as corn or, maize. Maize mazes can be large. Indoors, mirror mazes are another form of maze, in which many of the apparent pathways are imaginary routes seen through multiple reflections in mirrors. Another type of maze consists of a set of rooms linked by doors. Players enter at one spot, exit at another, or the idea may be to reach a certain spot in the maze. Mazes can be printed or drawn on paper to be followed by a pencil or fingertip.
Mazes can be built with snow. Maze generation is the act of designing the layout of walls within a maze. There are many different approaches to generating mazes, with various maze generation algorithms for building them, either by hand or automatically by computer. There are two main mechanisms used to generate mazes. In "carving passages", one marks out the network of available routes. In building a maze by "adding walls", one lays out a set of obstructions within an open area. Most mazes drawn on paper are done by drawing the walls, with the spaces in between the markings composing the passages. Maze solving is the act of finding a route through the maze from the start to finish; some maze solving methods are designed to be used inside the maze by a traveler with no prior knowledge of the maze, whereas others are designed to be used by a person or computer program that can see the whole maze at once. The mathematician Leonhard Euler was one of the first to analyze plane mazes mathematically, in doing so made the first significant contributions to the branch of mathematics known as topology.
Mazes containing no loops are known as "standard", or "perfect" mazes, are equivalent to a tree in graph theory. Thus many maze solving algorithms are related to graph theory. Intuitively, if one pulled and stretched out the paths in the maze in the proper way, the result could be made to resemble a tree. Mazes are used in psychology experiments to study spatial navigation and learning; such experiments use rats or mice. Examples are: Barnes maze Morris water maze Oasis maze Radial arm maze Elevated plus maze T-maze Ball-in-a-maze puzzles Dexterity puzzles which involve navigating a ball through a maze or labyrinth. Block maze A maze in which the player must clear the maze pathway by positioning blocks. Blocks may be added. Hamilton maze A maze. Linear or railroad maze A maze in which the paths are laid out like a railroad with switches and crossovers. Solvers are constrained to moving only forward. A railroad maze will have a single track for entrance and exit. Logic mazes These are like standard mazes except they use rules other than "don't cross the lines" to restrict motion.
Loops and traps maze A maze. The doors can lead to the correct path or create traps that divert you from the correct path and lead you to the starting point; the player may not return through a door through which he has entered, so dead ends may be created. The path is a series of loops interrupted by doors. Through the use of reciprocal doors, the correct path can intersect the incorrect path on a single plane. A graphical variant of this maze type is an arrow maze. Mazes in higher dimensions It is possible for a maze to have three or more dimensions. A maze with bridges is three-dimensional, some natural cave systems are three-dimensional mazes; the computer game Descent uses three-dimensional mazes. Any maze can be mapped into a higher dimension without changing its topology. Number maze A maze in which numbers are used to determine jumps that form a pathway, allowing the maze to criss-cross itself many times. Picture maze A standard maze. Turf mazes and mizmazes A pattern like a long rope folded up, without any crossings.
Numerous mazes of different kinds have been drawn, published in books and periodicals, used in advertising, in software, sold as art. In the 1970s there occurred a publishing "maze craze" in which numerous books, some magazines, were commercially available in nationwide outlets and devoted to mazes of a complexity, able to challenge adults as well as children; some of the best-selling books in the 1970s and early 1980s included those produced by Vladimir Koziakin and Glory Brightfield, Dave Phillips, Larry Evans, Greg Bright. Koziakin's works were predominantly of the standard two-dimensional "trace a line between the walls" variety; the works of the Brightfields had a similar two-dimensional form but used a variety of graphics-oriented "path obscuring" techniques. Although the routing was comparable to or simpler than Koziakin's mazes, the Brightfields' mazes did not allow the various pathway options to be discerned by the roving eye
Sudoku is a logic-based, combinatorial number-placement puzzle. The objective is to fill a 9×9 grid with digits so that each column, each row, each of the nine 3×3 subgrids that compose the grid contain all of the digits from 1 to 9; the puzzle setter provides a completed grid, which for a well-posed puzzle has a single solution. Completed games are always a type of Latin square with an additional constraint on the contents of individual regions. For example, the same single integer may not appear twice in the same row, column, or any of the nine 3×3 subregions of the 9×9 playing board. French newspapers featured variations of the puzzles in the 19th century, the puzzle has appeared since 1979 in puzzle books under the name Number Place. However, the modern Sudoku only started to become mainstream in 1986 by the Japanese puzzle company Nikoli, under the name Sudoku, meaning "single number", it first appeared in a US newspaper and The Times in 2004, from the efforts of Wayne Gould, who devised a computer program to produce distinct puzzles.
Number puzzles appeared in newspapers in the late 19th century, when French puzzle setters began experimenting with removing numbers from magic squares. Le Siècle, a Paris daily, published a completed 9×9 magic square with 3×3 subsquares on November 19, 1892, it was not a Sudoku because it contained double-digit numbers and required arithmetic rather than logic to solve, but it shared key characteristics: each row and subsquare added up to the same number. On July 6, 1895, Le Siècle's rival, La France, refined the puzzle so that it was a modern Sudoku, it simplified the 9×9 magic square puzzle so that each row and broken diagonals contained only the numbers 1–9, but did not mark the subsquares. Although they are unmarked, each 3×3 subsquare does indeed comprise the numbers 1–9 and the additional constraint on the broken diagonals leads to only one solution; these weekly puzzles were a feature of French newspapers such as L'Echo de Paris for about a decade, but disappeared about the time of World War I.
The modern Sudoku was most designed anonymously by Howard Garns, a 74-year-old retired architect and freelance puzzle constructor from Connersville and first published in 1979 by Dell Magazines as Number Place. Garns's name was always present on the list of contributors in issues of Dell Pencil Puzzles and Word Games that included Number Place, was always absent from issues that did not, he died in 1989 before getting a chance to see his creation as a worldwide phenomenon. Whether or not Garns was familiar with any of the French newspapers listed above is unclear; the puzzle was introduced in Japan by Nikoli in the paper Monthly Nikolist in April 1984 as Sūji wa dokushin ni kagiru, which can be translated as "the digits must be single" or "the digits are limited to one occurrence". At a date, the name was abbreviated to Sudoku by Maki Kaji, taking only the first kanji of compound words to form a shorter version. "Sudoku" is a registered trademark in Japan and the puzzle is referred to as Number Place or, more informally, a portmanteau of the two words, Num Pla.
In 1986, Nikoli introduced two innovations: the number of givens was restricted to no more than 32, puzzles became "symmetrical". It is now published in mainstream Japanese periodicals, such as the Asahi Shimbun. In 1997, Hong Kong judge Wayne Gould saw a completed puzzle in a Japanese bookshop. Over six years, he developed a computer program to produce unique puzzles rapidly. Knowing that British newspapers have a long history of publishing crosswords and other puzzles, he promoted Sudoku to The Times in Britain, which launched it on November 12, 2004; the first letter to The Times regarding Su Doku was published the following day on November 13 from Ian Payn of Brentford, complaining that the puzzle had caused him to miss his stop on the tube. Sudoku puzzles spread to other newspapers as a regular feature; the rapid rise of Sudoku in Britain from relative obscurity to a front-page feature in national newspapers attracted commentary in the media and parody. Recognizing the different psychological appeals of easy and difficult puzzles, The Times introduced both, side by side, on June 20, 2005.
From July 2005, Channel 4 included a daily Sudoku game in their teletext service. On August 2, the BBC's program guide Radio Times featured a weekly Super Sudoku with a 16×16 grid. In the United States, the first newspaper to publish a Sudoku puzzle by Wayne Gould was The Conway Daily Sun, in 2004; the world's first live TV Sudoku show, Sudoku Live, was a puzzle contest first broadcast on July 1, 2005, on Sky One. It was presented by Carol Vorderman. Nine teams of nine players representing geographical regions competed to solve a puzzle; each player had a hand-held device for entering numbers corresponding to answers for four cells. Phil Kollin of Winchelsea, was the series grand prize winner, taking home over £23,000 over a series of games; the audience at home was in a separate interactive competition, won by Hannah Withey of Cheshire. In 2005, the BBC launched SUDO-Q, a game show that combined Sudoku with general knowledge. However, it used only 4 × 6 × 6 puzzles. Four seasons were produced before
Word games are spoken or board games designed to test ability with language or to explore its properties. Word games are used as a source of entertainment, but can additionally serve an educational purpose. Young children can enjoy playing games such as Hangman, while developing important language skills like spelling. While Hangman is a dark game, what we like to focus on is the development of the children. Researchers have found that adults who solved crossword puzzles, which require familiarity with a larger vocabulary, had better brain function in life. Popular word-based game shows have been a part of television and radio throughout broadcast history, including Spelling Bee and Wheel of Fortune. In a letter arrangement game, the goal is to form words out of given letters; these games test vocabulary skills as well as lateral thinking skills. Some examples of letter arrangement games include Scrabble, Bananagrams and Paperback. In a paper and pencil game, players write their own words under specific constraints.
For example, a crossword requires players to use clues to fill out a grid, with words intersecting at specific letters. Other examples of paper and pencil games include Hangman and word searches. Semantic games focus on the semantics of words, utilising their meanings and the shared knowledge of players as a mechanic. Mad Libs, Blankety Blank, Codenames are all semantic games; as part of the modern "Golden Age" of board games, designers have created a variety of newer, non-traditional word games with more complex rules. Games like Codenames and Anomia were all designed after 2010, have earned widespread acclaim. Mobile games like Words with Friends and Word Connect have brought word games to modern audiences. Many popular word games have been adapted to radio game shows; as well as the examples given above, shows like Lingo, Says You!, Only Connect either revolve around or include elements of word games. Ambigrams Fortunately, Unfortunately Rebuses – picture puzzles representing a word Verbal arithmetic Anagram dictionary Double entendre Fortunately, Unfortunately Language game List of puzzle video games Online word game Phono-semantic matching Puns Puzzles Word play Word Ways: The Journal of Recreational Linguistics
Puzzle video game
Puzzle video games make up a unique genre of video games that emphasize puzzle solving. The types of puzzles can test many problem-solving skills including logic, pattern recognition, sequence solving, word completion; the player may have unlimited time or infinite attempts to solve a puzzle, or there may be a time limit, or simpler puzzles may be made difficult by having to complete them in real time, as in Tetris. The genre is broad, but it involves some level of abstraction and may make use of colors, numbers, physics, or complex rules. Unlike many video games, puzzle video games do make use of "lives" that challenge a player by limiting the number of tries. In puzzle video games, players try for a high score or to progress to the next level by getting to a certain place or achieving some criteria. Puzzle games focus on logical and conceptual challenges the possibility of a zero sum game is present, although the games add time-pressure or other action-elements. Although many action games and adventure games involve puzzles such as obtaining inaccessible objects, a true puzzle game focuses on puzzle solving as the primary gameplay activity.
Games involve shapes, colors, or symbols, the player must directly or indirectly manipulate them into a specific pattern. Rather than presenting a random collection of puzzles to solve, puzzle games offer a series of related puzzles that are a variation on a single theme; this theme could involve logic, or understanding a process. These games have a simple set of rules, where players manipulate game pieces on a grid, network or other interaction space. Players must unravel clues in order to achieve some victory condition, which will allow them to advance to the next level. Completing each puzzle will lead to a more difficult challenge, although some games avoid exhausting the player by offering easier levels between more difficult ones. In adventure games, some stages require solving puzzles as a way to advance the story. There is a large variety of puzzle game types; some feed to the player a random assortment of blocks or pieces that they must organize in the correct manner, such as Tetris and Lumines.
Others present a preset game board or pieces and challenge the player to solve the puzzle by achieving a goal. Puzzle games are easy to develop and adapt, being implemented on dedicated arcade units, home video game consoles, personal digital assistants, mobile phones. An action puzzle or arcade puzzle requires that the player manipulates game pieces in a real-time environment on a single screen and with a time limit, to solve the puzzle or clear the level; this is a broad term, used to describe several subsets of puzzle game. Firstly, it includes falling-block puzzles such as Tetris and KLAX, it includes games with characters moving through an environment, controlled either directly or indirectly. This can cross-over with other action genres: a platform game which requires a novel mechanic to complete levels might be a "puzzle platformer", such as manipulating time in Braid, it includes other action games that require timing and accuracy with pattern-matching or logic skills, such as the first-person Portal and The Talos Principle.
Other notable action puzzle games include Team Ico's Ico, a linear, story driven game with puzzles based around traversing puzzle environments while protecting a helpless companion. Made by Team Ico is Shadow of the Colossus, a game in which the player solves puzzles that involve finding and exploiting the weaknesses of giant beasts in combat. Nintendo's The Legend of Zelda: Breath of the Wild is another example of an action puzzle game, the primary objective being to seek out and solve physics-based puzzles which offer helpful upgrades for defeating the final boss. A hidden object game is a genre of puzzle video game in which the player must find items from a list that are hidden within a picture. Hidden object games are a popular trend in casual gaming, are comparatively inexpensive to buy. Time-limited trial versions of these games are available for download. An early hidden object game was Alice: An Interactive Museum. Computer Gaming World reported in 1993 that "one disadvantage of searching through screen after screen for'switches' is that after a while one develops a case of'clickitus' of the fingers as one punches that mouse button like a chicken pecking at a farmyard".
Other early incarnations are the video game adaptations of the I Spy books published by Scholastic Corporation since 1997. Publishers of hidden object games include Sandlot Games, Big Fish Games, Awem Studio, SpinTop Games, Codeminion. Examples of hidden object game series include Awakening, Antique Road Trip, Dream Chronicles, Mortimer Beckett, Mystery Trackers, Hidden Expedition and Mystery Case Files. A reveal the picture game is a type of puzzle game that features piece-by-piece revealing of a photo or picture. A free online example is PicTAPr. A physics game is a type of puzzle video game wherein the player must use the game's physics to complete each puzzle. Physics games use realistic physics to make games more challenging; the genre is popular in online flash games and mobile games. Educators have used these games to demonstrate principles of physics. Popular physics games include The Incredible Machine, World of Goo, Crayon Physics Deluxe, Angry Birds, Cut the Rope, Portal, Portal 2, Monster Strike and The Talos Principle.
In tile-matching video games, the player manipulates tiles in o
Henry Ernest Dudeney was an English author and mathematician who specialised in logic puzzles and mathematical games. He is known as one of the country's foremost creators of mathematical puzzles. Dudeney was born in the village of Mayfield, East Sussex, one of six children of Gilbert and Lucy Dudeney, his grandfather, John Dudeney, was well shepherd. Dudeney learned to play chess at an early age, continued to play throughout his life; this led to a marked interest in the composition of puzzles. Chess problems in particular fascinated him during his early years. Although Dudeney spent his career in the Civil Service, he continued to devise various problems and puzzles. Dudeney's first puzzle contributions were submissions to newspapers and magazines under the pseudonym of "Sphinx." Much of this earlier work was a collaboration with American puzzlist Sam Loyd. Dudeney contributed puzzles under his real name to publications such as The Weekly Dispatch, The Queen and Cassell's Magazine. For twenty years, he had a successful column, "Perplexities", in The Strand Magazine, edited by the former editor of Tit-Bits, George Newnes.
Dudeney continued to exchange puzzles with fellow recreational mathematician Sam Loyd for a while, but broke off the correspondence and accused Loyd of stealing his puzzles and publishing them under his own name. Some of Dudeney's most famous innovations were his 1903 success at solving the Haberdasher's Puzzle and publishing the first known crossnumber puzzle, in 1926, he has been credited with discovering new applications of digital roots. Dudeney was a leading exponent of verbal arithmetic puzzles, it had been claimed that he was the inventor of verbal arithmetic. This was refuted by the counter example of a verbal arithmetic puzzle published in the US in 1864. Omission of detailed puzzle rules in the cited farm journal, suggests they were popular in America by 1864, when Dudeney was 7 years old; the popularity of these puzzles guarantees they'd be well known by to Sam Loyd, an American puzzler and early Dudeney puzzle collaborator. Loyd has gained notoriety for his own claims of invention now exposed as false.
He claimed to have invented the verbal arithmetic puzzle. For another example of Loyd's pervasive deceit, see 15 puzzle. Dudeney experienced Loyd's duplicity and intellectual theft first hand publicly equating Loyd with the Devil. Both Dudeney and Loyd were featured by Martin Gardner in his Mathematical Games column in Scientific American—Loyd in August 1957 and Dudeney in June 1958. In 1884 Dudeney married Alice Whiffin, she became a well known writer who published many novels as well as a number of short stories in Harper's Magazine under the name "Mrs. Henry Dudeney". In her day, she was compared to Thomas Hardy for her portrayals of regional life; the income generated by her books was important to the Dudeney household, her fame gained them entry to both literary and court circles. After losing their first child at the age of four months in 1887, the Dudeneys had one daughter, Margery Janet, she married Christopher Fulleylove, son of John Fulleylove and one of an esteemed family of English artists.
The Fulleyloves emigrated to North America, first living in Canada and settling first in Oakland and New York. They had three sons: John Gabriel, James Shirley, Julian John. Alice's personal diaries were edited by Diana Crook and published in 1998 under the title A Lewes Diary: 1916–1944, they give a lively picture of her attempts to balance her literary career with her marriage to her brilliant but volatile husband. In April 1930, Dudeney died of throat cancer in Lewes, where he and his wife had moved in 1914 after a period of separation to rekindle their marriage. Alice Dudeney died on 21 November 1945, after a stroke. Both are buried in the Lewes town cemetery, their grave is marked by a copy of an 18th-century Sussex sandstone obelisk, which Alice had copied after Ernest's death to serve as their mutual tombstone. The Canterbury Puzzles Amusements in Mathematics The World's Best Word Puzzles Modern Puzzles Puzzles and Curious Problems A Puzzle-Mine Dudeney number Works by Henry Ernest Dudeney at Project Gutenberg Works by or about Henry Dudeney at Internet Archive The Haberdasher Puzzle O'Connor, John J..