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Tiling Puzzle
Tiling puzzles are puzzles involving two-dimensional packing problems in which a number of flat shapes have to be assembled into a larger given shape without overlaps (and often without gaps). Some tiling puzzles ask you to dissect a given shape first and then rearrange the pieces into another shape. Other tiling puzzles ask you to dissect a given shape while fulfilling certain conditions. The two latter types of tiling puzzles are also called dissection puzzles. Tiling puzzles may be made from wood, metal, cardboard, plastic or any other sheet-material. Many tiling puzzles are now available as computer games. Tiling puzzles have a long history. Some of the oldest and most famous are jigsaw puzzles and the tangram puzzle. Other examples of tiling puzzles include: * Conway puzzle * Domino tiling, of which the mutilated chessboard problem is one example * Eternity puzzle * Geometric magic square * Puzz-3D * Squaring the square * Tantrix * T puzzle Many three-dimensio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chinese Sunset
Chinese can refer to: * Something related to China * Chinese people, people of Chinese nationality, citizenship, and/or ethnicity **''Zhonghua minzu'', the supra-ethnic concept of the Chinese nation ** List of ethnic groups in China, people of various ethnicities in contemporary China ** Han Chinese, the largest ethnic group in the world and the majority ethnic group in Mainland China, Hong Kong, Macau, Taiwan, and Singapore ** Ethnic minorities in China, people of non-Han Chinese ethnicities in modern China ** Ethnic groups in Chinese history, people of various ethnicities in historical China ** Nationals of the People's Republic of China ** Nationals of the Republic of China ** Overseas Chinese, Chinese people residing outside the territories of Mainland China, Hong Kong, Macau, and Taiwan * Sinitic languages, the major branch of the Sino-Tibetan language family ** Chinese language, a group of related languages spoken predominantly in China, sharing a written script (Chi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mutilated Chessboard Problem
The mutilated chessboard problem is a tiling puzzle posed by Max Black in 1946 that asks: Suppose a standard 8×8 chessboard (or checkerboard) has two diagonally opposite corners removed, leaving 62 squares. Is it possible to place 31 dominoes of size 2×1 so as to cover all of these squares? It is an impossible puzzle: there is no domino tiling meeting these conditions. One proof of its impossibility uses the fact that, with the corners removed, the chessboard has 32 squares of one color and 30 of the other, but each domino must cover equally many squares of each color. More generally, if any two squares are removed from the chessboard, the rest can be tiled by dominoes if and only if the removed squares are of different colors. This problem has been used as a test case for automated reasoning, creativity, and the philosophy of mathematics. History The mutilated chessboard problem is an instance of domino tiling of grids and polyominoes, also known as "dimer models", a gen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wang Tile
Wang tiles (or Wang dominoes), first proposed by mathematician, logician, and philosopher Hao Wang in 1961, are a class of formal systems. They are modelled visually by square tiles with a color on each side. A set of such tiles is selected, and copies of the tiles are arranged side by side with matching colors, ''without'' rotating or reflecting them. The basic question about a set of Wang tiles is whether it can tile the plane or not, i.e., whether an entire infinite plane can be filled this way. The next question is whether this can be done in a periodic pattern. Domino problem In 1961, Wang conjectured that if a finite set of Wang tiles can tile the plane, then there also exists a ''periodic'' tiling, which, mathematically, is a tiling that is invariant under translations by vectors in a 2-dimensional lattice. This can be likened to the periodic tiling in a wallpaper pattern, where the overall pattern is a repetition of some smaller pattern. He also observed that this con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tessellation
A tessellation or tiling is the covering of a surface, often a plane (mathematics), plane, using one or more geometric shapes, called ''tiles'', with no overlaps and no gaps. In mathematics, tessellation can be generalized to high-dimensional spaces, higher dimensions and a variety of geometries. A periodic tiling has a repeating pattern. Some special kinds include ''regular tilings'' with regular polygonal tiles all of the same shape, and ''semiregular tilings'' with regular tiles of more than one shape and with every corner identically arranged. The patterns formed by periodic tilings can be categorized into 17 wallpaper groups. A tiling that lacks a repeating pattern is called "non-periodic". An ''aperiodic tiling'' uses a small set of tile shapes that cannot form a repeating pattern. A ''tessellation of space'', also known as a space filling or honeycomb, can be defined in the geometry of higher dimensions. A real physical tessellation is a tiling made of materials such a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sliding Puzzle
A sliding puzzle, sliding block puzzle, or sliding tile puzzle is a combination puzzle that challenges a player to slide (frequently flat) pieces along certain routes (usually on a board) to establish a certain end-configuration. The pieces to be moved may consist of simple shapes, or they may be imprinted with colours, patterns, sections of a larger picture (like a jigsaw puzzle), numbers, or letters. Sliding puzzles are essentially two-dimensional in nature, even if the sliding is facilitated by mechanically interlinked pieces (like partially encaged marbles) or three-dimensional tokens. In manufactured wood and plastic products, the linking and encaging is often achieved in combination, through mortise-and-tenon key channels along the edges of the pieces. In at least one vintage case of the popular Chinese cognate game Huarong Road, a wire screen prevents lifting of the pieces, which remain loose. As the illustration shows, some sliding puzzles are mechanical puzzles. Howev ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polyform
In recreational mathematics, a polyform is a plane (mathematics), plane figure or solid compound constructed by joining together identical basic polygons. The basic polygon is often (but not necessarily) a convex polygon, convex plane-filling polygon, such as a Square (geometry), square or a triangle. More specific names have been given to polyforms resulting from specific basic polygons, as detailed in the table below. For example, a square basic polygon results in the well-known polyominoes. Construction rules The rules for joining the polygons together may vary, and must therefore be stated for each distinct type of polyform. Generally, however, the following rules apply: #Two basic polygons may be joined only along a common edge, and must share the entirety of that edge. #No two basic polygons may overlap. #A polyform must be connected (that is, all one piece; see connected graph, connected space). Configurations of disconnected basic polygons do not qualify as polyforms. #The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dissection Puzzle
A dissection puzzle, also 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 also 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. History Dissection puzzles are an early form of geometric puzzle. The earliest known descriptions of dissection puzzles are from the time of Plato (427–347 BCE) in Ancient Greece, and 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 (see square trisection). A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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. While puzzles of this type have been in use by humanity as early as the 3rd century BC, one of the most well-known mechanical puzzles of modern day is the Rubik's Cube, invented by the Hungarian architect Ernő Rubik in 1974. The puzzles are typically designed for a single player, where the goal is for the player to see through the principle of the object, rather than accidentally coming up with the right solution through trial and error. With this in mind, they are often used as an intelligence test or in problem solving training. History 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, and the aim was to create different shapes from these pieces. This is not easy to do. (see Ostomachion loculus Archimedius) In Iran "puzzle-lo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
T Puzzle
The T puzzle is a tiling puzzle consisting of four polygonal shapes which can be put together to form a capital T. The four pieces are usually one isosceles right triangle, two right trapezoids and an irregular shaped pentagon. Despite its apparent simplicity, it is a surprisingly hard puzzle of which the crux is the positioning of the irregular shaped piece. The earliest T puzzles date from around 1900 and were distributed as promotional giveaways. From the 1920s wooden specimen were produced and made available commercially. Most T puzzles come with a leaflet with additional figures to be constructed. Which shapes can be formed depends on the relative proportions of the different pieces. Origins and early history The Latin Cross The Latin cross puzzle consists of a reassembling a five-piece dissection of the cross with three isosceles right triangles, one right trapezoids and an irregular shaped six-sized piece (see figure). When the pieces of the cross puzzle have the right d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tantrix
''Tantrix'' is a hexagonal tile-based abstract game invented by Mike McManaway from New Zealand. Each of the 56 different tiles in the set contains three lines, going from one edge of the tile to another. No two lines on a tile have the same colour. There are four colours in the set: red, yellow, blue, and green. No two tiles are identical, and each is individually numbered from 1 through 56. Gameplay In the multiplayer version of the game, each player chooses a colour, so there are between two and four players. Each draws one tile from the bag, and the person who draws the highest number goes first. Each player then takes five more tiles from the bag, and places all six tiles face up in front of them. The first person plays one tile, usually with their colour on it. Play then rotates clockwise. After playing a tile, each player takes a replacement tile from the bag, so that they always have six in front of them. Tiles played must match the colour of the edges adjoining i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Squaring The Square
Squaring the square is the problem of tiling an integral square using only other integral squares. (An integral square is a square whose sides have integer length.) The name was coined in a humorous analogy with squaring the circle. Squaring the square is an easy task unless additional conditions are set. The most studied restriction is that the squaring be perfect, meaning the sizes of the smaller squares are all different. A related problem is squaring the plane, which can be done even with the restriction that each natural number occurs exactly once as a size of a square in the tiling. The order of a squared square is its number of constituent squares. Perfect squared squares A "perfect" squared square is a square such that each of the smaller squares has a different size. It is first recorded as being studied by R. L. Brooks, C. A. B. Smith, A. H. Stone and W. T. Tutte at Cambridge University between 1936 and 1938. They transformed the square tiling into an equivalent el ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Puzz-3D
''Puzz 3D'' is the brand name of three-dimensional jigsaw puzzles, manufactured by Hasbro and formerly by Wrebbit, Inc. Unlike traditional puzzles which are composed of series of flat pieces that when put together, create a single unified image, the ''Puzz 3D'' series of puzzles are composed on plastic foam, with part of an image graphed on a stiff paper facade glued to the underlying foam piece and cut to match the piece's dimensions. When the pieces are put together, they create a standing structure. History Puzz 3D puzzles, invented by Paul Gallant, were first made in 1991 under the Quebec-based company Wrebbit. Throughout the 1990s, three-dimensional puzzles were made, leading to a rapid growth in the company. In 1993, Hasbro's Milton Bradley Company bought Wrebbit's Puzz 3D Line, and in 2005 Hasbro themselves completely bought Wrebbit, in 2006, moved the manufacture of Wrebbit's puzzles to its East Longmeadow, Massachusetts facility. The last series made under Hasbro was ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
