The strategy we will use to generate a sudoku puzzle is to start with a full board. If a negative number exists, then the solver tries to solve the puzzle with the assumption that the number at that position cannot exist. The solver also accepts negative numbers being present on the board. This function has been made quite general and has the capacity to solve sudoku puzzles of arbitrary size. I will make use of SparseArray to represent the initial sudoku puzzle, building on the “ Sudoku Game” example for LinearOptimization: Each 3×3 block (shown as gray or white blocks) must contain all the numbers 1–9.Īpplying these three rules, the player must now fill the board such that none of the rules are violated. Each column must contain all the numbers 1–9.ģ. Each row must contain all the numbers 1–9.Ģ. The player is supposed to fill the empty spots with numbers between 1 and 9 to if it’s an board) on the board following three rules:ġ. This is an example of a standard sudoku board: In a typical sudoku game, the player is presented with a 9×9 grid/board with some numbers exposed in certain positions of the board. To add to that discussion, I will demonstrate several features that are new to Mathematica Version 12.1, including how this game can be solved as an integer optimization problem using the function LinearOptimization, as well as how you can generate new sudoku games. Solving sudoku problems has long been discussed on Wolfram Community, and there has been some fantastic code presented to solve sudoku problems. Sudoku is a popular game that pushes the player’s analytical, mathematical and mental abilities.
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