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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. The game can be generalised even further from the above variants by playing on an arbitrary hypergraph where rows are hyperedges and cells are 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, Gobblet, Order and Chaos, Toss Across, and 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 move them around to empty spaces to keep playing. The game's grid ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Order And Chaos
Order and Chaos is a variant of the game tic-tac-toe on a 6×6 . It was invented by Stephen Sniderman and introduced by him in ''Games'' magazine in 1981. The player ''Order'' strives to create a five-in-a-row of either Xs or Os. The opponent ''Chaos'' endeavors to prevent this. Game rules Unlike typical board games, both players control both sets of pieces (Xs and Os). The game starts with the . Order plays first, then turns alternate. On each turn, a player places either an X or an O on any open square. Once played, pieces cannot be moved, thus Order and Chaos can be played using pencil and paper. Order aims to get five like pieces in a row either vertically, horizontally, or diagonally. Chaos aims to fill the board without completion of a line of five like pieces. Rules addition The original rules in ''Games'' magazine implied that six-in-a-row also wins. That version of the game was claimed weakly solved as a forced win for Order. The inventor has subsequently suggested a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magic Square
In recreational mathematics, a square array of numbers, usually positive integers, is called a magic square if the sums of the numbers in each row, each column, and both main diagonals are the same. The 'order' of the magic square is the number of integers along one side (''n''), and the constant sum is called the ' magic constant'. If the array includes just the positive integers 1,2,...,n^2, the magic square is said to be 'normal'. Some authors take magic square to mean normal magic square. Magic squares that include repeated entries do not fall under this definition and are referred to as 'trivial'. Some well-known examples, including the Sagrada Família magic square and the Parker square are trivial in this sense. When all the rows and columns but not both diagonals sum to the magic constant this gives a ''semimagic square (sometimes called orthomagic square). The mathematical study of magic squares typically deals with their construction, classification, and enumeration. A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Number Scrabble
Number Scrabble (also known as Pick15 or 3 to 15) is a mathematical game where players take turns to select numbers from 1 to 9 without repeating any numbers previously used, and the first player with a sum of exactly 15 using any three of their number selections wins the game. The game is isomorphic to tic-tac-toe Tic-tac-toe (American English), noughts and crosses (Commonwealth English), or Xs and Os (Canadian or Irish English) is a paper-and-pencil game for two players who take turns marking the spaces in a three-by-three grid with ''X'' or ''O''. ..., as can be seen if the game is mapped onto a magic square. Play Number Scrabble is played with the list of numbers between 1 and 9. Each player takes turns picking a number from the list. Once a number has been picked, it cannot be picked again. If a player has picked three numbers that add up to 15, that player wins the game. However, if all the numbers are used and no player gets exactly 15, the game is a draw. Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Isomorphic
In mathematics, an isomorphism is a structure-preserving mapping 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 isomorphism is derived from the Ancient Greek: ἴσος ''isos'' "equal", and μορφή ''morphe'' "form" or "shape". 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 be identified. In mathematical jargon, one says that two objects are . An automorphism is an isomorphism from a structure to itself. An isomorphism between two structures is a canonical isomorphism (a canonical map that is an isomorphism) if there is only one isomorphism between the two structures (as it is the case for solutions of a univer ... [...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 games c ... [...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 take ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Misère
Misère ( French for "destitution"), misere, bettel, betl, or (German for "beggar"; equivalent terms in other languages include , , ) 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 bidding can ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oren Patashnik
Oren Patashnik (born 1954) is an American computer scientist. He is notable for co-creating BibTeX, and co-writing '' Concrete Mathematics: A Foundation for Computer Science''. He is a researcher at the Center for Communications Research, La Jolla, and lives nearby in San Diego. Oren and his wife Amy have three children, Josh, Ariel, and Jeremy. History Oren Patashnik graduated from Yale University in 1976, and later became a doctoral student in computer science at Stanford University, where his research was supervised by Donald Knuth. 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 a notable 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 doc ... [...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 and/or computer assistance. Overview A two-player game can be solved on several levels: ;Ultra-weak : 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 moves of the perfect play. ;Weak : Provide an algorithm that secures a win for one player, or a draw for either, against any possible moves by the opponent, from the beginning of the game. ;Strong : Provide an algorithm that can produce perfect moves from any position, even if mistakes have already been made on one or b ... [...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 1950's 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 i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
