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- Toads and Frogs (Sapos y Ranas) es un juego combinatorio y partisano inventado por Richard Guy. Este juego matemático se utilizó como juego introductorio en el libro Winning Ways for your Mathematical Plays. Conocido por su simplicidad y la elegancia de sus reglas, Toads-and-Frogs es útil para ilustrar los conceptos principales de la teoría de juegos combinatorios. En particular, no es difícil evaluar juegos simples que involucran solo un sapo y una rana, construyendo el árbol de juego de la posición inicial. Sin embargo, se sabe que el caso general de evaluar una posición arbitraria es NP-difícil. Hay algunas conjeturas abiertas sobre el valor de algunas posiciones notables. También se ha considerado una versión del juego de rompecabezas para un jugador. (es)
- The combinatorial game Toads and Frogs is a partisan game invented by Richard Guy. This mathematical game was used as an introductory game in the book Winning Ways for your Mathematical Plays. Known for its simplicity and the elegance of its rules, Toads-and-Frogs is useful to illustrate the main concepts of combinatorial game theory. In particular, it is not difficult to evaluate simple games involving only one toad and one frog, by constructing the game tree of the starting position. However, the general case of evaluating an arbitrary position is known to be NP-hard. There are some open conjectures on the value of some remarkable positions. A one-player puzzle version of the game has also been considered. (en)
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- Toads and Frogs (Sapos y Ranas) es un juego combinatorio y partisano inventado por Richard Guy. Este juego matemático se utilizó como juego introductorio en el libro Winning Ways for your Mathematical Plays. También se ha considerado una versión del juego de rompecabezas para un jugador. (es)
- The combinatorial game Toads and Frogs is a partisan game invented by Richard Guy. This mathematical game was used as an introductory game in the book Winning Ways for your Mathematical Plays. Known for its simplicity and the elegance of its rules, Toads-and-Frogs is useful to illustrate the main concepts of combinatorial game theory. In particular, it is not difficult to evaluate simple games involving only one toad and one frog, by constructing the game tree of the starting position. However, the general case of evaluating an arbitrary position is known to be NP-hard. There are some open conjectures on the value of some remarkable positions. (en)
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- Sapos y Ranas (es)
- Toads and Frogs (en)
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