sudoku 数独

Objective

Fill a 9x9 grid with digits

Rules

1. Each row contains the numbers 1 to 9
2. Each column contains the numbers 1 to 9
3. Each box contains the numbers 1 to 9

Binary Constraint Satisfaction Problem

Variables

Variable for each tile in the sudoku grid with a total of 81 variables. Variable is a combination of a letter indicating the row, and a digit indicating the column.

X = {X₁, X₂, ..., X₈₁}

Domains

Each variable X_i has the domain of the digits [1,9]

D = {D₁, D₂, ..., D₈₁}

D_i = {1, 2, 3, 4, 5, 6, 7, 8, 9}

Constraints

The value of each variable X_i cannot be equal to any value in its:

• Row
• Column
• Box