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Tic-tac-toe Variants
Tic-tac-toe is an instance of an m,n,k-game, where two players alternate taking turns on an ''m''×''n'' board until one of them gets ''k'' in a row. Harary's generalized tic-tac-toe is an even broader generalization. The game can also be generalized as a Nd game, nd game. The game can be generalised even further from the above variants by playing on an arbitrary hypergraph where rows are hyperedges and cells are vertex (graph theory), vertices. Many board games share the element of trying to be the first to get ''n''-in-a-row, including three men's morris, nine men's morris, pente, gomoku, Qubic, Connect Four, Quarto (board game), Quarto, Gobblet, Order and Chaos, Toss Across, and Mojo (board game), Mojo. Variants of tic-tac-toe date back several millennia. Historic An early variation of tic-tac-toe was played in the Roman Empire, around the first century BC. It was called Terni Lapilli and instead of having any number of pieces, each player only had three; thus, they had to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gobblet
''Gobblet'' is a board game for two players designed by Thierry Denoual and published in 2001 by Gigamic and Blue Orange Games. Gobblet was a finalist for the 2004 Jeu de l'année The Jeu de l'année (French for ''Game of the Year'') was a French games award, given by the ''Association de Promotion et d'Evaluation des Jeux'' in October to outstanding parlour games * published during the previous year * published in the French .... The game is played on a 4×4 board. Each player has 12 pieces of the same colour but different sizes. Players take turns to place a piece on the board or move their piece that already is on the board. Bigger pieces can be placed so that they cover smaller ones. A player wins by placing four pieces of the same colour in a horizontal, vertical, or diagonal row. In 2003, Gigamic and Blue Orange Games released Gobblet Junior, a version of the game for younger players, which is played on a 3×3 board. In 2009, Blue Orange Games published revisioned edit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Isomorphic
In mathematics, an isomorphism is a structure-preserving mapping or morphism between two structures of the same type that can be reversed by an inverse mapping. Two mathematical structures are isomorphic if an isomorphism exists between them. The word is derived . The interest in isomorphisms lies in the fact that two isomorphic objects have the same properties (excluding further information such as additional structure or names of objects). Thus isomorphic structures cannot be distinguished from the point of view of structure only, and may often be identified. In mathematical jargon, one says that two objects are the same up to an isomorphism. A common example where isomorphic structures cannot be identified is when the structures are substructures of a larger one. For example, all subspaces of dimension one of a vector space are isomorphic and cannot be identified. An automorphism is an isomorphism from a structure to itself. An isomorphism between two structures is a c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ultimate Tic-tac-toe
Ultimate tic-tac-toe (also known as UTT, super tic-tac-toe, meta tic-tac-toe, (tic-tac-toe)², strategic tic-tac-toe, or Ultimate Noughts and Crosses) is a board game composed of nine tic-tac-toe boards arranged in a 3 × 3 grid. Players take turns playing on the smaller tic-tac-toe boards until one of them wins on the larger board. Compared to traditional tic-tac-toe, strategy in this game is conceptually more difficult and has proven more challenging for computers. Rules Just like in regular tic-tac-toe, the two players (X and O) take turns, starting with X. The game starts with X playing wherever they want in any of the 81 empty spots. Thereafter, each player moves in the small board corresponding to the position of the previous move in its small board, as indicated in the figures. If a move is played so that it wins a small board by the rules of normal tic-tac-toe, then the entire small board is marked as won by the player in the larger board. Once a small board ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Impartial Game
In combinatorial game theory, an impartial game is a game in which the allowable moves depend only on the position and not on which of the two players is currently moving, and where the payoffs are symmetric. In other words, the only difference between player 1 and player 2 is that player 1 goes first. The game is played until a terminal position is reached. A terminal position is one from which no moves are possible. Then one of the players is declared the winner and the other the loser. Furthermore, impartial games are played with perfect information and no chance moves, meaning all information about the game and operations for both players are visible to both players. Impartial games include Nim, Sprouts, Kayles, Quarto, Cram, Chomp, Subtract a square, Notakto, and poset games. Go and chess are not impartial, as each player can only place or move pieces of their own color. Games such as poker, dice or dominos are not impartial games as they rely on chance. Impartial ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Notakto
Notakto is a tic-tac-toe variant, also known as neutral or impartial tic-tac-toe. The game is a combination of the games tic-tac-toe and Nim, played across one or several boards with both of the players playing the same piece (an "X" or cross). The game ends when all the boards contain a three-in-a-row of Xs, at which point the player to have made the last move loses the game. However, in this game, unlike tic-tac-toe, there will always be a player who wins any game of Notakto. Notakto is an impartial game, where the allowable moves depend only on the state of the game and not on which player is taking their turn. When played across multiple boards it is a disjunctive game. The game is attributed to professor and backgammon player Bob Koca, who is said to have invented the game in 2010, when his five-year-old nephew suggested playing a game of tic-tac-toe with both players as "X". Play Notakto is played on a finite number of empty three-by-three boards. Then, each player tak ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Misère
Misère ( French for "destitution"), misere, nullo, bettel, betl, or (German for "beggar"; equivalent terms in other languages include , and ) is a bid in various card games, and the player who bids misère undertakes to win no tricks or as few as possible, usually at no trump, in the round to be played. This does not allow sufficient variety to constitute a game in its own right, but it is the basis of such trick-avoidance games as Hearts, and provides an optional contract for most games involving an auction. The term or category may also be used for some card game of its own with the same aim, like Black Peter. A misère bid usually indicates an extremely poor hand, hence the name. An open or lay down misère, or misère ouvert is a 500 bid where the player is so sure of losing every trick that they undertake to do so with their cards placed face-up on the table. Consequently, 'lay down misère' is Australian gambling slang for a predicted easy victory. In Skat, the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oren Patashnik
Oren Patashnik (born 1954) is an American computer scientist. He co-created BibTeX, and co-authored '' Concrete Mathematics: A Foundation for Computer Science''. While working at Bell Labs in 1980, Patashnik proved that Qubic can always be won by the first player. Using 1500 hours of computer time, Patashnik's proof is an early example of a computer-assisted proof. In 1985, Patashnik created the bibliography-system, BibTeX, in collaboration with Leslie Lamport, the creator of LaTeX. LaTeX is a system and programming language for formatting documents, which is especially designed for mathematical documents. BibTeX is a widely used bibliography-formatting tool for LaTeX. Patashnik assisted Ronald Graham and Donald Knuth in writing the 1988 textbook '' Concrete Mathematics: A Foundation for Computer Science''. Patashnik became a doctoral student of Andrew Yao at Stanford University Leland Stanford Junior University, commonly referred to as Stanford University, is a Private ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Solved Board Games
A solved game is a game whose outcome (win, lose or draw) can be correctly predicted from any position, assuming that both players play perfectly. This concept is usually applied to abstract strategy games, and especially to games with full information and no element of chance; solving such a game may use combinatorial game theory or computer assistance. Overview A two-player game can be solved on several levels: Ultra-weak solution : Prove whether the first player will win, lose or draw from the initial position, given perfect play on both sides . This can be a non-constructive proof (possibly involving a strategy-stealing argument) that need not actually determine any details of the perfect play. Weak solution : Provide one algorithm for each of the two players, such that the player using it can achieve at least the optimal outcome, regardless of the opponent's moves, from the start of the game, using reasonable computational resources. Strong solution : Provide an algorithm t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ancient Egypt
Ancient Egypt () was a cradle of civilization concentrated along the lower reaches of the Nile River in Northeast Africa. It emerged from prehistoric Egypt around 3150BC (according to conventional Egyptian chronology), when Upper and Lower Egypt were amalgamated by Menes, who is believed by the majority of List of Egyptologists, Egyptologists to have been the same person as Narmer. The history of ancient Egypt unfolded as a series of stable kingdoms interspersed by the "Periodization of ancient Egypt, Intermediate Periods" of relative instability. These stable kingdoms existed in one of three periods: the Old Kingdom of Egypt, Old Kingdom of the Early Bronze Age; the Middle Kingdom of Egypt, Middle Kingdom of the Middle Bronze Age; or the New Kingdom of Egypt, New Kingdom of the Late Bronze Age. The pinnacle of ancient Egyptian power was achieved during the New Kingdom, which extended its rule to much of Nubia and a considerable portion of the Levant. After this period, Egypt ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Claudia Zaslavsky
Claudia Zaslavsky (January 12, 1917 – January 13, 2006) was an American mathematics teacher and ethnomathematician. Life She was born Claudia Natoma Cohen (later changed to Cogan) on January 12, 1917, in Upper Manhattan in New York City and grew up in Allentown, Pennsylvania. She attributed her first interest in mathematics to her early childhood experiences when she helped her parents in their dry goods store. She studied mathematics at Hunter College and then earned a master's degree in statistics at the University of Michigan. In the 1950s while raising her children she was the bookkeeper at Chelsea Publishing Co. and taught pre-instrument classes to small children. Math teacher She became a mathematics teacher at Woodlands High School in Hartsdale, New York. She pursued postgraduate study in mathematics education at Teachers College, Columbia University, in 1974–1978. During that time she sought to learn about mathematics in Africa to better capture the inte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Roman Empire
The Roman Empire ruled the Mediterranean and much of Europe, Western Asia and North Africa. The Roman people, Romans conquered most of this during the Roman Republic, Republic, and it was ruled by emperors following Octavian's assumption of effective sole rule in 27 BC. The Western Roman Empire, western empire collapsed in 476 AD, but the Byzantine Empire, eastern empire lasted until the fall of Constantinople in 1453. By 100 BC, the city of Rome had expanded its rule from the Italian peninsula to most of the Mediterranean Sea, Mediterranean and beyond. However, it was severely destabilised by List of Roman civil wars and revolts, civil wars and political conflicts, which culminated in the Wars of Augustus, victory of Octavian over Mark Antony and Cleopatra at the Battle of Actium in 31 BC, and the subsequent conquest of the Ptolemaic Kingdom in Egypt. In 27 BC, the Roman Senate granted Octavian overarching military power () and the new title of ''Augustus (title), Augustus'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
