Entropy Minimization for Solving Sudoku

Abstract

Solving Sudoku puzzles is formulated as an optimization problem over a set of probabilities. The constraints for a given puzzle translate into a convex polyhedral feasible set for the probabilities. The solution to the puzzle lies at an extremal point of the polyhedron where the probabilities are either zero or one and the entropy is zero. Because the entropy is positive at all other feasible points, an entropy minimization approach is adopted to solve Sudoku. To escape local entropy minima at nonsolution extremal points, a search procedure is proposed in which each iteration involves solving a simple convex optimization problem. This approach is evaluated on thousands of puzzles spanning four levels of difficulty from “easy” to “evil”.