A 9 X9 SUDOKU puzzle has the following rules. Each row and column must contain numbers between 1 and 9, and each inner box must contain numbers between 1 and 9. Each column and row and each sub-box should contain each number only once.

Let’s just define Xijk to be 1 for all values โโof I, j and k from 1 to 9. If cell (I, j) contains an integer k where I, j and k all range between 1 and 9. Here I point out. denotes the ith row and j denotes the jth column and k denotes an integer between 1 and 9. When X134 = 1, it means cell (1,3) contains number 4. This would also mean that none of the other elements except cell (1,3) in the first row or third column can be equal to 4.

We will use a total of 729 variables to model SUDOKU.

Let us now formulate each of the three classes of rules algebraically.

Each row should contain a number between 1 and 9 only once.

For the first row, this rule will appear as (called “constraint” in the language…