![]() ![]() A domino placed on the chessboard will always cover one white square and one black square. In the philosophy of mathematics, it has been examined in studies of the nature of mathematical proof. It has also been studied in cognitive science as a test case for creative insight, Black's original motivation for the problem. The use of the mutilated chessboard problem in automated reasoning stems from a proposal for its use by John McCarthy in 1964. Golomb (1954), George Gamow and Marvin Stern (1958), Claude Berge (1958), and Martin Gardner in his Scientific American column " Mathematical Games" (1957). It was popularized in the 1950s through later discussions by Solomon W. The mutilated chessboard problem itself was proposed by philosopher Max Black in his book Critical Thinking (1946), with a hint at the coloring-based solution to its impossibility. Domino tilings also have a long history of practical use in pavement design and the arrangement of tatami flooring. Fowler and George Stanley Rushbrooke in 1937. The mutilated chessboard problem is an instance of domino tiling of grids and polyominoes, also known as "dimer models", a general class of problems whose study in statistical mechanics dates to the work of Ralph H.
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