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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. [1] Harary's generalized tic-tac-toe is an even broader generalization. The game can also be generalized as a n d game. [2] The game can be generalised even further from the above variants by playing on an ...
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. The player who succeeds in placing three of their marks in a horizontal, vertical, or diagonal row is the winner.
Game tree. In the context of combinatorial game theory, which typically studies sequential games with perfect information, a game tree is a graph representing all possible game states within such a game. Such games include well-known ones such as chess, checkers, Go, and tic-tac-toe. This can be used to measure the complexity of a game, as it ...
Tic tac toe is a classic game. How to win tic tac toe requires strategic thinking and planning to win the game or force a draw. When you’re the first one up, there is a simple strategy on how to ...
Top part of Tic-tac-toe game tree. Breadth-first search ( BFS) is an algorithm for searching a tree data structure for a node that satisfies a given property. It starts at the tree root and explores all nodes at the present depth prior to moving on to the nodes at the next depth level. Extra memory, usually a queue, is needed to keep track of ...
Notakto is a tic-tac-toe variant, also known as neutral or impartial tic-tac-toe. [ 1][ 2] The game is a combination of the games tic-tac-toe and Nim, [ 1][ 3] 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, [ 4][ 5][ 6] at ...
(Note that the line 13, 22, 31, while a valid line for the game tic-tac-toe, is not considered a combinatorial line.) In this particular case, the Hales–Jewett theorem does not apply; it is possible to divide the tic-tac-toe board into two sets, e.g. {11, 22, 23, 31} and {12, 13, 21, 32, 33}, neither of which contain a combinatorial line (and ...
A strategy-stealing argument can be used on the example of the game of tic-tac-toe, for a board and winning rows of any size. Suppose that the second player (P2) is using a strategy S which guarantees a win. The first player (P1) places an X in an arbitrary position. P2 responds by placing an O according to S.