The following image shows a challenging Sudoku puzzle.
A sudoku puzzle solution must satisfy the following rules.
- Each row contains the numbers 1-9 exactly once.
- Each column contains the numbers 1-9 exactly once.
- If we divide the grid into 9 subsquares by grouping rows/columns (0-2), (3-5), and (6-8), each subsquare has the numbers 1-9 exactly once.
Use the framework code provided to solve the Sudoku puzzle shown above. The rules listed describe three different types of constraints. The first two constraints must be added to the constrained quadratic model to complete the exercise.
The code provided includes an initial definition of variables to be used.
Binary variables have been defined as x[i][j][k], where i indicates the row
index, j indicates the column index, and k+1 indicates a digit from 1-9.
Using this description, we define x[i][j][k] == 1 if the entry in row i,
column j equals digit k+1.
Note that since Python list indices start at 0 and sudoku digits range from
1-9 we must use index k to represent digit k+1.