Latin squares: Leonhard Euler, Quasigroup, Latin square, Mathematics of Sudoku, Graeco-Latin square, R. C. Bose, Circulant matrix - Softcover

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9781156778074: Latin squares: Leonhard Euler, Quasigroup, Latin square, Mathematics of Sudoku, Graeco-Latin square, R. C. Bose, Circulant matrix

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 27. Chapters: Leonhard Euler, Quasigroup, Latin square, Mathematics of Sudoku, Graeco-Latin square, R. C. Bose, Circulant matrix, Problems in Latin squares, Latin hypercube sampling, Small Latin squares and quasigroups, Hyper-Graeco-Latin square design, Sharadchandra Shankar Shrikhande, Futoshiki, E. T. Parker, Dinitz conjecture, Thirty-six officers problem, Latin square property, Latin rectangle. Excerpt: The class of Sudoku puzzles consists of a partially completed row-column grid of cells partitioned into N regions each of size N cells, to be filled in using a prescribed set of N distinct symbols (typically the numbers ), so that each row, column and region contains exactly one of each element of the set. The puzzle can be investigated using mathematics. The mathematical analysis of Sudoku falls into two main areas: analyzing the properties of a) completed grids and b) puzzles. Grid analysis has largely focused on counting (enumerating) possible solutions for different variants. Puzzle analysis centers on the initial given values. The techniques used in either are largely the same: combinatorics and permutation group theory, augmented by the dexterous application of programming tools. There are many Sudoku variants, (partially) characterized by the size (N) and shape of their regions. For classic Sudoku, N=9 and the regions are 3x3 squares (called blocks or boxes). A rectangular Sudoku uses rectangular regions of row-column dimension R×C. For R×1 (and 1×C), i.e. where the region is a row or column, Sudoku becomes a Latin square. Other Sudoku variants also exist, such as those with irregularly-shaped regions or with additional constraints (hypercube) or different (Samunamupure) constraint types. See Sudoku - Variants for a discussion of variants and Sudoku terms and jargon for an expanded listing. The mathematics of Sudoku is a...

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 27. Chapters: Leonhard Euler, Quasigroup, Latin square, Mathematics of Sudoku, Graeco-Latin square, R. C. Bose, Circulant matrix, Problems in Latin squares, Latin hypercube sampling, Small Latin squares and quasigroups, Hyper-Graeco-Latin square design, Sharadchandra Shankar Shrikhande, Futoshiki, E. T. Parker, Dinitz conjecture, Thirty-six officers problem, Latin square property, Latin rectangle. Excerpt: The class of Sudoku puzzles consists of a partially completed row-column grid of cells partitioned into N regions each of size N cells, to be filled in using a prescribed set of N distinct symbols (typically the numbers ), so that each row, column and region contains exactly one of each element of the set. The puzzle can be investigated using mathematics. The mathematical analysis of Sudoku falls into two main areas: analyzing the properties of a) completed grids and b) puzzles. Grid analysis has largely focused on counting (enumerating) possible solutions for different variants. Puzzle analysis centers on the initial given values. The techniques used in either are largely the same: combinatorics and permutation group theory, augmented by the dexterous application of programming tools. There are many Sudoku variants, (partially) characterized by the size (N) and shape of their regions. For classic Sudoku, N=9 and the regions are 3x3 squares (called blocks or boxes). A rectangular Sudoku uses rectangular regions of row-column dimension R×C. For R×1 (and 1×C), i.e. where the region is a row or column, Sudoku becomes a Latin square. Other Sudoku variants also exist, such as those with irregularly-shaped regions or with additional constraints (hypercube) or different (Samunamupure) constraint types. See Sudoku - Variants for a discussion of variants and Sudoku terms and jargon for an expanded listing. The mathematics of Sudoku is a...

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