Riddle
A riddle is a statement or question or phrase having a double or veiled meaning, put forth as a puzzle to be solved. Riddles are of two types: enigmas, which are problems expressed in metaphorical or allegorical language that require ingenuity and careful thinking for their solution, conundra, which are questions relying for their effects on punning in either the question or the answer. Archer Taylor says that "we can say that riddling is a universal art" and cites riddles from hundreds of different cultures including Finnish, American Indian, Russian and Filipino sources amongst many others. Many riddles and riddle-themes are internationally widespread. However, at least in the West, if not more "riddles have in the past few decades ceased to be part of oral tradition", being replaced by other oral-literary forms, by other tests of wit such as quizzes. In the assessment of Elli Köngas Maranda, whereas myths serve to encode and establish social norms, "riddles make a point of playing with conceptual boundaries and crossing them for the intellectual pleasure of showing that things are not quite as stable as they seem" – though the point of doing so may still be to "play with boundaries, but to affirm them".
Defining riddles is hard and has attracted a fair amount of scholarly debate. The first major modern attempt to define the riddle was by Robert Petsch in 1899, with another seminal contribution, inspired by structuralism, by Robert A. Georges and Alan Dundes in 1963. Georges and Dundes suggested that "a riddle is a traditional verbal expression which contains one or more descriptive elements, a pair of which may be in opposition. There are many possible sub-sets of the riddle, including charades and some jokes. In some traditions and contexts, riddles may overlap with proverbs; the Russian phrase "Nothing hurts it, but it groans all the time" can be deployed as a proverb or as a riddle. Much academic research on riddles has focused on collecting, cataloguing and typologising riddles. Key work on cataloguing and typologising riddles was published by Antti Aarne in 1918–20, by Archer Taylor. In the case of ancient riddles recorded without solutions, considerable scholarly energy goes into proposing and debating solutions.
Whereas researchers had tended to take riddles out of their social performance contexts, the rise of anthropology in the post-War period encouraged more researchers to study the social role of riddles and riddling. However, wide-ranging studies of riddles have tended to be limited to Western countries, with Oriental and African riddles being neglected. Riddles have attracted linguists studying riddles from the point of view of semiotics. Many riddles appear in similar form across many countries, continents. Borrowing of riddles happens on a small, local scale, across great distances. Dorvlo gives an example of a riddle, borrowed from the Ewe language by speakers of the neighboring Logba language: "This woman has not been to the riverside for water, but there is water in her tank"; the answer is a coconut. On a much wider scale, the Riddle of the Sphinx has been documented in the Marshall Islands carried there by Western contacts in the last two centuries. Key examples of internationally widespread riddles, with a focus on European tradition, based on the classic study by Antti Aarne.
The basic form of this riddle is'White field, black seeds', where the field is a page and the seeds are letters. An example is the eighth- or ninth-century Veronese Riddle: Here, the oxen are the scribe's finger and thumb, the plough is the pen. Among literary riddles, riddles on the pen and other writing equipment are widespread; this type is found across Eurasia. For example, a riddle in the Sanskrit Rig Veda describes a'twelve-spoked wheel, upon which stand 720 sons of one birth'; the most famous example of this type is the Riddle of the Sphinx. This Estonian example shows the pattern: The riddle describes a crawling baby, a standing person, an old person with a walking stick; this type includes riddles along the lines of this German example: The conceit here is that Two-legs is a person, Three-legs is a three-legged stool, Four-legs is a dog, One-leg is a walking stick. An example of this type is given here in thirteenth-century Icelandic form: The cow has four udders, four legs, two horns, two back legs, one tail.
This is a French version of the type. An English version is: Here, a snowflake falls from the sky, is blown off by the wind; the riddle was at times a prominent literary form in the ancient and medieval world, so riddles are extensively, if patchily, attested in our written records from these periods. According to Archer Taylor, "the oldest recorded riddles are Babylonian school texts which show no literary polish"; the answers to the riddles are not preserved. "It is clear that we have here riddles from oral tradition that a teacher has put into a schoolbook." It is thought. "The Sanskrit term that most close
Sudoku
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
Pythagorean theorem
In mathematics, the Pythagorean theorem known as Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the square of the hypotenuse is equal to the sum of the squares of the other two sides; the theorem can be written as an equation relating the lengths of the sides a, b and c called the "Pythagorean equation": a 2 + b 2 = c 2, where c represents the length of the hypotenuse and a and b the lengths of the triangle's other two sides. Although it is argued that knowledge of the theorem predates him, the theorem is named after the ancient Greek mathematician Pythagoras as it is he who, by tradition, is credited with its first proof, although no evidence of it exists. There is some evidence that Babylonian mathematicians understood the formula, although little of it indicates an application within a mathematical framework. Mesopotamian and Chinese mathematicians all discovered the theorem independently and, in some cases, provided proofs for special cases.
The theorem has been given numerous proofs – the most for any mathematical theorem. They are diverse, including both geometric proofs and algebraic proofs, with some dating back thousands of years; the theorem can be generalized in various ways, including higher-dimensional spaces, to spaces that are not Euclidean, to objects that are not right triangles, indeed, to objects that are not triangles at all, but n-dimensional solids. The Pythagorean theorem has attracted interest outside mathematics as a symbol of mathematical abstruseness, mystique, or intellectual power; the Pythagorean theorem was known long before Pythagoras, but he may well have been the first to prove it. In any event, the proof attributed to him is simple, is called a proof by rearrangement; the two large squares shown in the figure each contain four identical triangles, the only difference between the two large squares is that the triangles are arranged differently. Therefore, the white space within each of the two large squares must have equal area.
Equating the area of the white space yields the Pythagorean theorem, Q. E. D; that Pythagoras originated this simple proof is sometimes inferred from the writings of the Greek philosopher and mathematician Proclus. Several other proofs of this theorem are described below. If c denotes the length of the hypotenuse and a and b denote the lengths of the other two sides, the Pythagorean theorem can be expressed as the Pythagorean equation: a 2 + b 2 = c 2. If the length of both a and b are known c can be calculated as c = a 2 + b 2. If the length of the hypotenuse c and of one side are known the length of the other side can be calculated as a = c 2 − b 2 or b = c 2 − a 2; the Pythagorean equation relates the sides of a right triangle in a simple way, so that if the lengths of any two sides are known the length of the third side can be found. Another corollary of the theorem is that in any right triangle, the hypotenuse is greater than any one of the other sides, but less than their sum. A generalization of this theorem is the law of cosines, which allows the computation of the length of any side of any triangle, given the lengths of the other two sides and the angle between them.
If the angle between the other sides is a right angle, the law of cosines reduces to the Pythagorean equation. This theorem may have more known proofs than any other; this proof is based on the proportionality of the sides of two similar triangles, that is, upon the fact that the ratio of any two corresponding sides of similar triangles is the same regardless of the size of the triangles. Let ABC represent a right triangle, with the right angle located at C. Draw the altitude from point C, call H its intersection with the side AB. Point H divides the length of the hypotenuse c into parts d and e; the new triangle ACH is similar to triangle ABC, because they both have a right angle, they share the angle at A, meaning that the third angle will be the same in both triangles as well, marked as θ in the figure. By a similar reasoning, the triangle CBH is similar to ABC; the proof of similarity of the triangles requires the triangle postulate: the sum of the angles in a triangle is two right angles, is equivalent to the parallel postulate.
Similarity of the triangles leads to the equality of ratios of corresponding sides: B C A B = B H B C and A C A B = A H A C. The first result equates
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 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, or logic puzzles. Puzzles are created to be a form of entertainment but they can arise from serious mathematical or logistical problems. In such cases, their solution may be a significant contribution to mathematical research; the 1989 edition of the Oxford English Dictionary dates the word puzzle to the end of the 16th century. Its first documented use was in a book titled The Voyage of Robert Dudley...to the West Indies, 1594–95, narrated by Capt. Wyatt, by himself, by Abram Kendall, master; the word came to be used as a noun. The word puzzle comes from pusle, meaning "bewilder, confound", a frequentive of the obsolete verb pose in the sense of "perplex".
The use of the word to mean "a toy contrived to test one's ingenuity" is recent. Puzzles can be divided into categories. For example, a maze is a type of tour puzzle; some other categories are construction puzzles, stick puzzles, tiling puzzles, disentanglement puzzles, lock puzzles, folding puzzles, combination puzzles, mechanical puzzles. A chess problem is a puzzle. Examples are the eight queens puzzle. Jigsaw puzzles. Lateral thinking puzzles called "situation puzzles" Mathematical puzzles include the missing square puzzle and many impossible puzzles — puzzles which have no solution, such as the Seven Bridges of Königsberg, the three cups problem, three utilities problem Mechanical puzzles such as the Rubik's Cube and Soma cube Metapuzzles are puzzles which unite elements of other puzzles. Paper-and-pencil puzzles such as Uncle Art's Funland, connect the dots, nonograms Also the logic puzzles published by Nikoli: Sudoku, Kakuro, Hashiwokakero, Hitori, Light Up, Number Link, Ripple Effect and Kuromasu.
Peg solitaire. Rubik's Cube and other combination puzzles can be stimulating toys for children or recreational activities for adults. Sangaku Sliding puzzles such as the 15 Puzzle. Puzz-3D is a three-dimensional variant of this type. Sokoban Spot the difference Tangram Word puzzles, including anagrams, crossword puzzles and word search puzzles. Tabletop and digital word puzzles include Bananagrams, Bonza, Letterpress, Puzzlage, Ruzzle, Upwords, WordSpot, Words with Friends. Wheel of Fortune is a game show centered on a word puzzle. Solutions of puzzles require the recognition of patterns and the adherence to a particular kind of ordering. People with a high level of inductive reasoning aptitude may be better at solving such puzzles than others, but puzzles based upon inquiry and discovery may be solved more by those with good deduction skills. Deductive reasoning improves with practice. Mathematical puzzles involves BODMAS. BODMAS is an acronym and it stands for Bracket, Of, Multiplication and Subtraction.
In certain regions, PEDMAS is the synonym of BODMAS. It explains the order of operations to solve an expression; some mathematical puzzle requires Top to Bottom convention to avoid the ambiguity in the order of operations. It is an elegantly simple idea that relies, as sudoku does, on the requirement that numbers appear only once starting from top to bottom as coming along. Puzzle makers are people; some notable creators of puzzles are: Ernő Rubik Sam Loyd Henry Dudeney Boris Kordemsky David J. Bodycombe Will Shortz Lloyd King Martin Gardner Raymond Smullyan Jigsaw puzzles are the most popular form of puzzle. Jigsaw puzzles were invented around 1760, when John Spilsbury, a British engraver and cartographer, mounted a map on a sheet of wood, which he sawed around the outline of each individual country on the map, he used the resulting pieces as an aid for the teaching of geography. After becoming popular among the public, this kind of teaching aid remained the primary use of jigsaw puzzles until about 1820.
The largest puzzle is made by German game company Ravensburger. The smallest puzzle made was created at LaserZentrum Hannover, it is the size of a sand grain. By the early 20th century and newspapers had found that they could increase their readership by publishing puzzle contests, beginning with crosswords and in modern days sudoku. There are organizations and events that cater to puzzle enthusiasts, such as: Nob Yoshigahara Puzzle Design Competition World Puzzle Championship National Puzzlers' League Puzzlehunts such as the Maze of Games List of impossible puzzles List of Nikoli puzzle types Riddle Puzzles at DMOZ
Optical illusion
An optical illusion is an illusion caused by the visual system and characterized by a visual percept that appears to differ from reality. Illusions come in a wide variety. According to that, there are three main classes: physical and cognitive illusions, in each class there are four kinds: Ambiguities, distortions and fictions. A classical example for a physical distortion would be the apparent bending of a stick half immerged in water. An example for a physiological fiction is an afterimage. Three typical cognitive distortions are the Ponzo, Müller-Lyer illusion. Physical illusions are caused by e.g. by the optical properties of water. Physiological illusions arise in the eye or the visual pathway, e.g. from the effects of excessive stimulation of a specific receptor type. Cognitive visual illusions are the result of unconscious inferences and are those most known. Pathological visual illusions arise from pathological changes in the physiological visual perception mechanisms causing the aforementioned types of illusions.
A familiar phenomenon an example for a physical visual illusion are when mountains appear to be much nearer in clear weather with low humidity than they are. This is; the classical example of a physical illusion is when a stick, half immersed in water appears bent. This phenomenon has been discussed by Ptolemy and was a prototypical example for an illusion. Physiological illusions, such as the afterimages following bright lights, or adapting stimuli of excessively longer alternating patterns, are presumed to be the effects on the eyes or brain of excessive stimulation or interaction with contextual or competing stimuli of a specific type—brightness, position, size, etc; the theory is that a stimulus follows its individual dedicated neural path in the early stages of visual processing and that intense or repetitive activity in that or interaction with active adjoining channels causes a physiological imbalance that alters perception. The Hermann grid illusion and Mach bands are two illusions that are best explained using a biological approach.
Lateral inhibition, where in the receptive field of the retina light and dark receptors compete with one another to become active, has been used to explain why we see bands of increased brightness at the edge of a color difference when viewing Mach bands. Once a receptor is active, it inhibits adjacent receptors; this inhibition creates contrast. In the Hermann grid illusion the gray spots appear at the intersection because of the inhibitory response which occurs as a result of the increased dark surround. Lateral inhibition has been used to explain the Hermann grid illusion, but this has been disproved. More recent empirical approaches to optical illusions have had some success in explaining optical phenomena with which theories based on lateral inhibition have struggled. Cognitive illusions are assumed to arise by interaction with assumptions about the world, leading to "unconscious inferences", an idea first suggested in the 19th century by the German physicist and physician Hermann Helmholtz.
Cognitive illusions are divided into ambiguous illusions, distorting illusions, paradox illusions, or fiction illusions. Ambiguous illusions are pictures or objects that elicit a perceptual "switch" between the alternative interpretations; the Necker cube is a well-known example. Distorting or geometrical-optical illusions are characterized by distortions of size, position or curvature. A striking example is the Café wall illusion. Other examples are the famous Müller-Lyer illusion and Ponzo illusion. Paradox illusions are generated by objects that are paradoxical or impossible, such as the Penrose triangle or impossible staircase seen, for example, in M. C. Escher's Descending and Waterfall; the triangle is an illusion dependent on a cognitive misunderstanding. Fictions are when a figure is perceived though it is not in the stimulus. To make sense of the world it is necessary to organize incoming sensations into information, meaningful. Gestalt psychologists believe one way this is done is by perceiving individual sensory stimuli as a meaningful whole.
Gestalt organization can be used to explain many illusions including the rabbit–duck illusion where the image as a whole switches back and forth from being a duck being a rabbit and why in the figure–ground illusion the figure and ground are reversible. In addition, Gestalt theory can be used to explain the illusory contours in the Kanizsa's Triangle. A floating white triangle, which does not exist, is seen; the brain has a need to see familiar simple objects and has a tendency to create a "whole" image from individual elements. Gestalt means "form" or "shape" in German. However, another explanation of the Kanizsa's Triangle is based in evolutionary psychology and the fact that in order to survive it was important to see form and edges; the use of perceptual organization to create meaning out of stimuli is the principle behind other well-known illusions including impossible objects. Our brain makes sense of shapes and symbols putting them together like a jigsaw puzzle, formulating that which isn't there to that whi
Word game
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
Mechanical puzzle
A mechanical puzzle is a puzzle presented as a set of mechanically interlinked pieces in which the solution is to manipulate the whole object or parts of it. One of the most well-known mechanical puzzles is Ernő Rubik’s Cube that he invented in 1974; the puzzles are designed for a single player where the goal is for the player to see through the principle of the object, not so much that they accidentally come up with the right solution through trial and error. With this in mind, they are used as an intelligence test or in problem solving training; the oldest known mechanical puzzle comes from Greece and appeared in the 3rd century BC. The game consists of a square divided into 14 parts, the aim was to create different shapes from these pieces; this is not easy to do. In Iran "puzzle-locks" were made as early as the 17th century AD; the next known occurrence of puzzles is in Japan. In 1742 there is a mention of a game called "Sei Shona-gon Chie No-Ita" in a book. Around the year 1800 the Tangram puzzle from China became popular, 20 years it had spread through Europe and America.
The company Richter from Rudolstadt began producing large amounts of Tangram-like puzzles of different shapes, the so-called "Anker-puzzles" in about 1891. In 1893, Angelo John Lewis, using the pen name "Professor Hoffman", wrote, it contained, among other things, more than 40 descriptions of puzzles with secret opening mechanisms. This book grew into a reference work for puzzle games and modern copies exist for those interested; the beginning of the 20th century was a time in which puzzles were fashionable and the first patents for puzzles were recorded. With the invention of modern polymers manufacture of many puzzles became cheaper. In this category, the puzzle is present in component form, the aim is to produce a certain shape; the Soma cube made by Piet Hein, the Pentomino by Solomon Golomb and the aforementioned laying puzzles Tangram and "Anker-puzzles" are all examples of this type of puzzle. Furthermore, problems in which a number of pieces have to be arranged so as to fit into a box are classed in this category.
The image shows a variant of Hoffman's packing problem. The aim is to pack 27 cuboids with side lengths A, B, C into a box of side length A+B+C, subject to two constraints: 1) A, B, C must not be equal 2) The smallest of A, B, C must be larger than / 4 One possibility would be A=18, B=20, C=22 – the box would have to have the dimensions 60×60×60. Modern tools such as laser cutters allow the creation of complex two-dimensional puzzles made of wood or acrylic plastic. In recent times this has become predominant and puzzles of extraordinarily decorative geometry have been designed; this makes use of the multitude of ways of subdividing areas into repeating shapes. Computers aid in the design of new puzzles. A computer allows an exhaustive search for solution – with its help a puzzle may be designed in such a way that it has the fewest possible solutions, or a solution requiring the most steps possible; the consequence is that solving the puzzle can be difficult. The use of transparent materials enables the creation of puzzles, in which pieces have to be stacked on top of each other.
The aim is to create a specific image or colour scheme in the solution. For example, one puzzle consists of several discs in which angular sections of varying sizes are differently coloured; the discs have to be stacked so as to create a colour circle around the discs. The puzzles in this category are solved by opening or dividing them into pieces; this includes those puzzles with secret opening mechanisms, which are to be opened by trial and error. Furthermore, puzzles consisting of several metal pieces linked together in some fashion are considered part of this category; the two puzzles shown in the picture are good for social gatherings, since they appear to be easily taken apart, but in reality many people cannot solve this puzzle. The problem here lies in the shape of the interlocking pieces – the mating surfaces are tapered, thus can only be removed in one direction. However, each piece has two oppositely sloping tapers mating with the two adjoining pieces so that the piece cannot be removed in either direction.
Boxes called secret boxes or puzzle boxes with secret opening mechanisms popular in Japan, are included in this category. These caskets contain more or less complex invisible opening mechanisms which reveal a small hollow space on opening. There is a vast variety of opening mechanisms, such as hardly visible panels which need to be shifted, inclination mechanisms, magnetic locks, movable pins which need to be rotated into a certain position up and time locks in which an object has to be held in a given position until a liquid has filled up a certain container. In an interlocking puzzle, one or more pieces hold the rest together, or the pieces are mutually self-sustaining; the aim is to disassemble and reassemble the puzzle. Both assembly and disassembly can be difficult – contrary to assembly puzzles, these puzzles do not just fall apart easily; the level of difficulty is assessed in terms of the number of moves required to remove the first piece from the initial puzzle. Puzzles introduced elements of rotation.
The known history of these puzzles reaches back to the beginning of the 18th century. In 1803 a catalog by "Bastelmeier" contained two puzzles of this type. Professor Hoffman's puzzle book mentioned above contained two interlocking puzzles. At the beginning of the 19th century the Jap
