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Taking Sudoku Seriously: The Math Behind the World's Most Popular Pencil Puzzle is a book on the mathematics of Sudoku. It was written by Jason Rosenhouse and Laura Taalman , and published in 2011 by the Oxford University Press .
The following other wikis use this file: Usage on en.wikibooks.org Wikijunior:Maze and Drawing Book; Wikijunior:Maze and Drawing Book/Print version
When Sudoku is played with pencil and paper, possibilities are often called pencil marks. In the standard 9×9 Sudoku variant, in which each of 9×9 cells is assigned one of 9 numbers, there are 9×9×9=729 possibilities. Using obvious notation for rows, columns and numbers, the possibilities can be labeled R1C1#1, R1C1#2, …, R9C9#9.
A Sudoku whose regions are not (necessarily) square or rectangular is known as a Jigsaw Sudoku. In particular, an N × N square where N is prime can only be tiled with irregular N -ominoes . For small values of N the number of ways to tile the square (excluding symmetries) has been computed (sequence A172477 in the OEIS ). [ 10 ]
The constraints of Sudoku codes are non-linear: all symbols within a constraint (row, line, sub-grid) must be different from any other symbol within this constraint. Hence there is no all-zero codeword in Sudoku codes. Sudoku codes can be represented by probabilistic graphical model in which they take the form of a low-density parity-check code ...
A Sudoku may also be modelled as a constraint satisfaction problem. In his paper Sudoku as a Constraint Problem, [14] Helmut Simonis describes many reasoning algorithms based on constraints which can be applied to model and solve problems. Some constraint solvers include a method to model and solve Sudokus, and a program may require fewer than ...
Each row, column, or block of the Sudoku puzzle forms a clique in the Sudoku graph, whose size equals the number of symbols used to solve the puzzle. A graph coloring of the Sudoku graph using this number of colors (the minimum possible number of colors for this graph) can be interpreted as a solution to the puzzle.
If the maze is on paper, the thread may well be a pencil. Logic problems of all natures may be resolved via Ariadne's thread, the maze being but an example. At present, it is most prominently applied to Sudoku puzzles, used to attempt values for as-yet-unsolved cells. The medium of the thread for puzzle-solving can vary widely, from a pencil to ...
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