Sudoku is a simple/easy to define problem. You have a 9 x 9 grid and you have to fill the numbers 1 to 9 in such a way that no number is repeated in any row, column, or sub grid. This problem has been explored by a number of people in a number of different ways. Most popular of them all is Peter Norvig’s Solving Every Sudoku Puzzle.

Sudoku is a Constraint Satisfaction Problem (CSP). Most popular techniques for solving a CSP are Backtracking, Constraint Propagation and Search. In this post, we will explore solving Sudoku as a Mixed-Integer Programming problem using CVXPY. We will also use a SAT Solver to solve the problem.

In the MIP method, we use a dummy objective function to trick the solver into satisfying the constraints.

A SAT Solver is designed for problems like this. SAT is short for SATISFYABILITY or Boolean satisfiability problem.

Sudoku as MIP

Sudoku as SAT Problem