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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. The player who succeeds in placing three of their marks in a horizontal, vertical, or diagonal row is ...
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 ...
The winning row can be horizontal, vertical, or diagonal on a single board as in regular tic-tac-toe, or vertically in a column, or a diagonal line through four boards. As with traditional tic-tac-toe, several commercial sets of apparatus have been sold for the game, and it may also be played with pencil and paper with a hand-drawn board.
The pieces fall straight down, occupying the lowest available space within the column. The objective of the game is to be the first to form a horizontal, vertical, or diagonal line of four of one's own tokens. It is therefore a type of m,n,k-game (7, 6, 4) with restricted piece placement. Connect Four is a solved game. The first player can ...
A field of view. In first person video games, the field of view or field of vision (abbreviated FOV) is the extent of the observable game world that is seen on the display at any given moment. It is typically measured as an angle, although whether this angle is the horizontal, vertical, or diagonal component of the field of view varies from ...
Buffon's needle was the earliest problem in geometric probability to be solved; [2] it can be solved using integral geometry. The solution for the sought probability p, in the case where the needle length l is not greater than the width t of the strips, is. This can be used to design a Monte Carlo method for approximating the number π ...
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