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Hiroimono
Goishi Hiroi, also known as Hiroimono, is a Japanese variant of peg solitaire. In it, pegs (or stones on a Go board) are arranged in a set pattern, and the player must pick up all the pegs or stones, one by one. In some variants, the choice of the first stone is fixed, while in others the player is free to choose the first stone. After the first stone, each stone that is removed must be taken from the next occupied position along a vertical or horizontal line from the previously-removed stone. Additionally, it is not possible to reverse direction along a line: each step from one position to the next must either continue in the same direction as the previous step, or turn at a right angle from the previous step. These puzzles were used for bar bets in 14th-century Japan, and a collection of them was published in a Japanese puzzle book from 1727. Determining whether a given puzzle can be solved is NP-complete. This can be proved either by a many-one reduction from 3-satisfiability, or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Peg Solitaire
Peg solitaire, Solo Noble or simply Solitaire is a board game for one player involving movement of pegs on a board with holes. Some sets use marbles in a board with indentations. The game is known as solitaire in Britain and as peg solitaire in the US where 'solitaire' is now the common name for patience. It is also called Brainvita in India, where sets are sold commercially under this name. The first evidence of the game can be traced back to the court of Louis XIV, and the specific date of 1697, with an engraving made ten years later by Claude Auguste Berey of Anne de Rohan-Chabot, Princess of Soubise, with the puzzle by her side. The August 1697 edition of the French literary magazine '' Mercure galant'' contains a description of the board, rules and sample problems. This is the first known reference to the game in print. The standard game fills the entire board with pegs except for the central hole. The objective is, making valid moves, to empty the entire board except fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Go Board
Go equipment refers to the board, stones (playing pieces), and bowls for the stones required to play the game of Go. The quality and materials used in making Go equipment varies considerably, and the cost varies accordingly from economical to extremely expensive. History The oldest known surviving Go equipment is a board carved from rock that dates from the Han Dynasty in China. Other examples of ancient equipment can be found in museums in Japan and Korea. Equipment Board The Go board, called the ''goban'' in Japanese, is the playing surface on which to place the stones. The standard board is marked with a 19×19 grid. Smaller boards include a 13×13 grid and a 9×9 grid used for shorter games that are often used to teach beginners. Some 19×19 boards have a 13×13 grid on the reverse side. 17×17 was used in historical times. Chinese boards are generally square; Japanese and Korean boards are slightly longer than wide, so that they appear square when viewed from a normal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Right Angle
In geometry and trigonometry, a right angle is an angle of exactly 90 Degree (angle), degrees or radians corresponding to a quarter turn (geometry), turn. If a Line (mathematics)#Ray, ray is placed so that its endpoint is on a line and the adjacent angles are equal, then they are right angles. The term is a calque of Latin ''angulus rectus''; here ''rectus'' means "upright", referring to the vertical perpendicular to a horizontal base line. Closely related and important geometrical concepts are perpendicular lines, meaning lines that form right angles at their point of intersection, and orthogonality, which is the property of forming right angles, usually applied to Euclidean vector, vectors. The presence of a right angle in a triangle is the defining factor for right triangles, making the right angle basic to trigonometry. Etymology The meaning of ''right'' in ''right angle'' possibly refers to the Classical Latin, Latin adjective ''rectus'' 'erect, straight, upright, perp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bar Bet
A bar bet is a bet made between two patrons at a bar. Bar bets can range from wagers about little-known trivia, such as obscure historical facts, to feats of skill and strength. Some bar bets are intended to trick the other party into losing. Famous bar bets * The annual Midnight Sun baseball game played in Fairbanks, Alaska (the only game to be contested after midnight without the use of artificial lighting) was established in 1906 as the result of a bar bet. * Two of Tony Hawks' books, ''Round Ireland With A Fridge'' () and ''Playing The Moldovans At Tennis'' (), were written describing Hawks' attempts to win two bar bets. * The film ''To Have and Have Not'' is supposedly the result of bar bet between Ernest Hemingway and Howard Hawks, with Hemingway betting Hawks that Hawks couldn't make a good film from Hemingway's worst novel. * A common rumor claims that the creation of Scientology was the result of a bar bet between L. Ron Hubbard and Robert A. Heinlein. Richard Leiby, a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
NP-complete
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 de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Many-one Reduction
In computability theory and computational complexity theory, a many-one reduction (also called mapping reduction) is a reduction which converts instances of one decision problem L_1 into instances of a second decision problem L_2 where the instance reduced to is in the language L_2 if the initial instance was in its language L_1 and is not in the language L_2 if the initial instance was not in its language L_1. Thus if we can decide whether L_2 instances are in the language L_2, we can decide whether L_1 instances are in its language by applying the reduction and solving L_2. Thus, reductions can be used to measure the relative computational difficulty of two problems. It is said that L_1 reduces to L_2 if, in layman's terms L_2 is harder to solve than L_1. That is to say, any algorithm that solves L_2 can also be used as part of a (otherwise relatively simple) program that solves L_1. Many-one reductions are a special case and stronger form of Turing reductions. With many-one red ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
3-satisfiability
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] |
Parsimonious Reduction
In computational complexity theory and game complexity, a parsimonious reduction is a transformation from one problem to another (a reduction) that preserves the number of solutions. Informally, it is a bijection between the respective sets of solutions of two problems. A general reduction from problem A to problem B is a transformation that guarantees that whenever A has a solution B also has ''at least one'' solution and vice versa. A parsimonious reduction guarantees that for every solution of A, there exists ''a unique solution'' of B and vice versa. Parsimonious reductions are commonly used in computational complexity for proving the hardness of counting problems, for counting complexity classes such as #P. Additionally, they are used in game complexity, as a way to design hard puzzles that have a unique solution, as many types of puzzles require. Formal definition Let x be an instance of problem X. A ''Parsimonious reduction'' R from problem X to problem Y is a reductio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hamiltonian Path Problem
In the mathematical field of graph theory the Hamiltonian path problem and the Hamiltonian cycle problem are problems of determining whether a Hamiltonian path (a path in an undirected or directed graph that visits each vertex exactly once) or a Hamiltonian cycle exists in a given graph (whether directed or undirected). Both problems are NP-complete. The Hamiltonian cycle problem is a special case of the travelling salesman problem, obtained by setting the distance between two cities to one if they are adjacent and two otherwise, and verifying that the total distance travelled is equal to ''n'' (if so, the route is a Hamiltonian circuit; if there is no Hamiltonian circuit then the shortest route will be longer). Reduction between the path problem and the cycle problem The problems of finding a Hamiltonian path and a Hamiltonian cycle can be related as follows: * In one direction, the Hamiltonian path problem for graph ''G'' can be related to the Hamiltonian cycle problem in a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
