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Tentai Show
Tentai Show ( Japanese: 天体ショー ''tentai shō''), also known by the names Tentaisho, Galaxies, Spiral Galaxies, or Sym-a-Pix, is a binary-determination logic puzzle published by Nikoli. Rules Tentai Show is played on a rectangular grid of squares. On the grid are dots representing ''stars'', which can be found on the grid either on the center of a cell, an edge, or a corner. The objective of the puzzle is to draw lines along the dashed lines to divide the grid into regions representing ''galaxies''. In the resulting grid, all galaxies must have 180° rotational symmetry and contain exactly one dot located at its center. The colors of the dots do not affect the logic of the puzzle and can be ignored when solving. In puzzles with multiple colored dots, the regions of the finished grid may be colored with the corresponding dot colors to reveal a picture. Solution Methods Tentai Show puzzles can be solved using the following steps. # Draw walls between adjacent cells t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
10x10 Tentaisho Unsolved
1 (one, unit, unity) is a number representing a single or the only entity. 1 is also a numerical digit and represents a single unit of counting or measurement. For example, a line segment of ''unit length'' is a line segment of length 1. In conventions of sign where zero is considered neither positive nor negative, 1 is the first and smallest positive integer. It is also sometimes considered the first of the infinite sequence of natural numbers, followed by 2, although by other definitions 1 is the second natural number, following 0. The fundamental mathematical property of 1 is to be a multiplicative identity, meaning that any number multiplied by 1 equals the same number. Most if not all properties of 1 can be deduced from this. In advanced mathematics, a multiplicative identity is often denoted 1, even if it is not a number. 1 is by convention not considered a prime number; this was not universally accepted until the mid-20th century. Additionally, 1 is th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Japanese (language)
is spoken natively by about 128 million people, primarily by Japanese people and primarily in Japan, the only country where it is the national language. Japanese belongs to the Japonic or Japanese- Ryukyuan language family. There have been many attempts to group the Japonic languages with other families such as the Ainu, Austroasiatic, Koreanic, and the now-discredited Altaic, but none of these proposals has gained widespread acceptance. Little is known of the language's prehistory, or when it first appeared in Japan. Chinese documents from the 3rd century AD recorded a few Japanese words, but substantial Old Japanese texts did not appear until the 8th century. From the Heian period (794–1185), there was a massive influx of Sino-Japanese vocabulary into the language, affecting the phonology of Early Middle Japanese. Late Middle Japanese (1185–1600) saw extensive grammatical changes and the first appearance of European loanwords. The basis of the standard dialect moved f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logic Puzzle
A logic puzzle is a puzzle deriving from the mathematical field of deduction. History The logic puzzle was first produced by Charles Lutwidge Dodgson, who is better known under his pen name Lewis Carroll, the author of ''Alice's Adventures in Wonderland''. In his book ''The Game of Logic'' he introduced a game to solve problems such as confirming the conclusion "Some greyhounds are not fat" from the statements "No fat creatures run well" and "Some greyhounds run well". Puzzles like this, where we are given a list of premises and asked what can be deduced from them, are known as syllogisms. Dodgson goes on to construct much more complex puzzles consisting of up to 8 premises. In the second half of the 20th century mathematician Raymond M. Smullyan continued and expanded the branch of logic puzzles with books such as '' The Lady or the Tiger?'', '' To Mock a Mockingbird'' and ''Alice in Puzzle-Land''. He popularized the " knights and knaves" puzzles, which involve knights, who al ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nikoli (publisher)
is a Japanese publisher that specializes in games and, especially, logic puzzles. ''Nikoli'' is also the nickname of a quarterly magazine (whose full name is ''Puzzle Communication Nikoli'') issued by the company in Tokyo. ''Nikoli'' was established in 1980 and became prominent worldwide with the popularity of ''Sudoku''. The name "Nikoli" comes from the racehorse who won the Irish 2,000 Guineas in 1980; the founder of Nikoli, Maki Kaji, was fond of horseracing and betting. Nikoli's claim to fame is its vast library of "culture independent" puzzles. An example of a language/culture-dependent genre of puzzle would be the crossword, which relies on a specific language and alphabet. For this reason Nikoli's puzzles are often purely logical, and often numerical. Nikoli's Sudoku Sudoku (; ja, 数独, sūdoku, digit-single; originally called Number Place) is a logic-based, combinatorics, combinatorial number-placement puzzle. In classic Sudoku, the objective is to fill a 9 � ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rotational Symmetry
Rotational symmetry, also known as radial symmetry in geometry, is the property a shape has when it looks the same after some rotation by a partial turn. An object's degree of rotational symmetry is the number of distinct orientations in which it looks exactly the same for each rotation. Certain geometric objects are partially symmetrical when rotated at certain angles such as squares rotated 90°, however the only geometric objects that are fully rotationally symmetric at any angle are spheres, circles and other spheroids. Formal treatment Formally the rotational symmetry is symmetry with respect to some or all rotations in ''m''-dimensional Euclidean space. Rotations are direct isometries, i.e., isometries preserving orientation. Therefore, a symmetry group of rotational symmetry is a subgroup of ''E''+(''m'') (see Euclidean group). Symmetry with respect to all rotations about all points implies translational symmetry with respect to all translations, so space is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
NP-completeness
In computational complexity theory, a problem is NP-complete when: # it is a problem for which the correctness of each solution can be verified quickly (namely, in polynomial time) and a brute-force search algorithm can find a solution by trying all possible solutions. # the problem can be used to simulate every other problem for which we can verify quickly that a solution is correct. In this sense, NP-complete problems are the hardest of the problems to which solutions can be verified quickly. If we could find solutions of some NP-complete problem quickly, we could quickly find the solutions of every other problem to which a given solution can be easily verified. The name "NP-complete" is short for "nondeterministic polynomial-time complete". In this name, "nondeterministic" refers to nondeterministic Turing machines, a way of mathematically formalizing the idea of a brute-force search algorithm. Polynomial time refers to an amount of time that is considered "quick" for a det ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boolean Circuit
In computational complexity theory and circuit complexity, a Boolean circuit is a mathematical model for combinational digital logic circuits. A formal language can be decided by a family of Boolean circuits, one circuit for each possible input length. Boolean circuits are defined in terms of the logic gates they contain. For example, a circuit might contain binary AND and OR gates and unary NOT gates, or be entirely described by binary NAND gates. Each gate corresponds to some Boolean function that takes a fixed number of bits as input and outputs a single bit. Boolean circuits provide a model for many digital components used in computer engineering, including multiplexers, adders, and arithmetic logic units, but they exclude sequential logic. They are an abstraction that omits many aspects relevant to designing real digital logic circuits, such as metastability, fanout, glitches, power consumption, and propagation delay variability. Formal definition In giving a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boolean Satisfiability Problem
In logic and computer science, the Boolean satisfiability problem (sometimes called propositional satisfiability problem and abbreviated SATISFIABILITY, SAT or B-SAT) is the problem of determining if there exists an interpretation that satisfies a given Boolean formula. In other words, it asks whether the variables of a given Boolean formula can be consistently replaced by the values TRUE or FALSE in such a way that the formula evaluates to TRUE. If this is the case, the formula is called ''satisfiable''. On the other hand, if no such assignment exists, the function expressed by the formula is FALSE for all possible variable assignments and the formula is ''unsatisfiable''. For example, the formula "''a'' AND NOT ''b''" is satisfiable because one can find the values ''a'' = TRUE and ''b'' = FALSE, which make (''a'' AND NOT ''b'') = TRUE. In contrast, "''a'' AND NOT ''a''" is unsatisfiable. SAT is the first problem that was proved to be NP-complete; ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Planar SAT
In computer science, the planar 3-satisfiability problem (abbreviated PLANAR 3SAT or PL3SAT) is an extension of the classical Boolean 3-satisfiability problem to a planar incidence graph. In other words, it asks whether the variables of a given Boolean formula—whose incidence graph consisting of variables and clauses can be embedded on a plane—can be consistently replaced by the values TRUE or FALSE in such a way that the formula evaluates to TRUE. If this is the case, the formula is called ''satisfiable''. On the other hand, if no such assignment exists, the function expressed by the formula is FALSE for all possible variable assignments and the formula is ''unsatisfiable''. For example, the formula "''a'' AND NOT ''b''" is satisfiable because one can find the values ''a'' = TRUE and ''b'' = FALSE, which make (''a'' AND NOT ''b'') = TRUE. In contrast, "''a'' AND NOT ''a''" is unsatisfiable. Like 3SAT, PLANAR-SAT is NP-complete, and is co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Time Complexity
In computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly estimated by counting the number of elementary operations performed by the algorithm, supposing that each elementary operation takes a fixed amount of time to perform. Thus, the amount of time taken and the number of elementary operations performed by the algorithm are taken to be related by a constant factor. Since an algorithm's running time may vary among different inputs of the same size, one commonly considers the worst-case time complexity, which is the maximum amount of time required for inputs of a given size. Less common, and usually specified explicitly, is the average-case complexity, which is the average of the time taken on inputs of a given size (this makes sense because there are only a finite number of possible inputs of a given size). In both cases, the time complexity is generally express ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Nikoli Puzzle Types
is a Japanese publisher that specializes in games and, especially, logic puzzles. ''Nikoli'' is also the nickname of a quarterly magazine (whose full name is ''Puzzle Communication Nikoli'') issued by the company in Tokyo. ''Nikoli'' was established in 1980 and became prominent worldwide with the popularity of '' Sudoku''. The name "Nikoli" comes from the racehorse Horse racing is an equestrian performance sport, typically involving two or more horses ridden by jockeys (or sometimes driven without riders) over a set distance for competition. It is one of the most ancient of all sports, as its basic pr ... who won the Irish 2,000 Guineas in 1980; the founder of Nikoli, Maki Kaji, was fond of horseracing and betting. Nikoli's claim to fame is its vast library of "culture independent" puzzles. An example of a language/ culture-dependent genre of puzzle would be the crossword, which relies on a specific language and alphabet. For this reason Nikoli's puzzles are often p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
