Sudoku.
How does a Sudoku puzzle work?
The basic premise of solving a sudoku puzzle is to place the numbers one through nine exactly once in each row, column and 3×3 box based on the starting numbers that are already filled in and any subsequent numbers you fill in. This should be done by logic rather than guessing.
What is the goal of a sudoku puzzle?
In classic sudoku, the objective is to fill a 9×9 grid with digits so that each column, each row, and each of the nine 3×3 subgrids that compose the grid (also called “boxes”, “blocks”, or “regions”) contains all of the digits from 1 to 9.
How to solve Sudoku puzzles using integer programming?
The key idea is to transform a puzzle from a square 9-by-9 grid to a cubic 9-by-9-by-9 array of binary values (0 or 1). Think of the cubic array as being 9 square grids stacked on top of each other, where each layer corresponds to an integer from 1 through 9.
When do you need constraints to solve Sudoku?
The last constraint fixes that only one of a value is found in each subgrid. Even more constraints need to be specified when you are trying to solve any particular sudoku, namely the original starting state of each non-empty cell.
Which is the optimal objective value for sudoku?
LP: Optimal objective value is 405.000000. Optimal solution found. Intlinprog stopped at the root node because the objective value is within a gap tolerance of the optimal value, options.AbsoluteGapTolerance = 0 (the default value). The intcon variables are integer within tolerance, options.IntegerTolerance = 1e-05 (the default value).
What kind of puzzle has only one integer value?
A puzzle consists of filling in a nine-by-nine grid, such that each row, column, and three-by-three subgrid contains only one of an integer value. In other words, you are not allowed to enter another one in the first row, first column, or first subgrid of the “Hard 1” puzzle on the bottom left.
