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A single set of free tetrominoes or one-sided tetrominoes cannot fit in a rectangle. This can be shown with a proof similar to the mutilated chessboard argument . A 5×4 rectangle with a checkerboard pattern has 20 squares, containing 10 light squares and 10 dark squares, but a complete set of free tetrominoes has either 11 dark squares and 9 ...
A typical Tetris game screen. Tetris is a puzzle video game with a consistent general design across its numerous versions. [1] Tetris consists of a rectangular field of play in which one of seven tetromino pieces, [b] geometric shapes consisting of arranged four squares typically named after the letters they resemble, descend from the center-top.
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Tetris pieces I, J, L, O, S, T, Z. Consider the seven Tetris pieces (I, J, L, O, S, T, Z), known mathematically as the tetrominoes.If you consider all the possible rotations of these pieces — for example, if you consider the "I" oriented vertically to be distinct from the "I" oriented horizontally — then you find there are 19 distinct possible shapes to be displayed on the screen.
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Gardner proposed several simple games with a set of free pentominoes and a chessboard. Some variants of the Sudoku puzzle use nonomino-shaped regions on the grid. The video game Tetris is based on the seven one-sided tetrominoes (spelled "Tetriminos" in the game), and the board game Blokus uses all of the free polyominoes up to pentominoes.
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