Redundant Sudoku rules

Inequalities in 2x2-Sudoku and beyond

2×2-Sudoku (or ShiDoku) is a sized down variant of the usual 3×3-Sudoku puzzle. Its set of constraints contains 56 binary inequalities. It is proven that any maximal redundant set of these binary inequalities has size 16. This is in line with a conjecture about 3×3Sudoku. The result is achieved partly by rigorous proofs, partly by programming in Prolog. The generalization to N×N-Sudoku with N >...

Sudoku as a SAT Problem

Sudoku is a very simple and well-known puzzle that has achieved international popularity in the recent past. This paper addresses the problem of encoding Sudoku puzzles into conjunctive normal form (CNF), and subsequently solving them using polynomial-time propositional satisfiability (SAT) inference techniques. We introduce two straightforward SAT encodings for Sudoku: the minimal encoding and...

Solving Sudoku Using Combined Message Passing Algorithms

In this paper we apply message-passing algorithms to solve Sudoku puzzles. We provide explicit expression for the sum-product algorithm and the max-product algorithm and analyze the difference between the algorithms in terms of performance and efficiency. The failure of the max-product algorithm when been applied to Sudoku problem is due to the existence of stopping-sets. We show empirically th...

Solving Sudoku with Boolean Algebra

Sudoku is a very popular puzzle which consists of placing several numbers in a squared grid according to some simple rules. In this paper, we present a Sudoku solving technique named Boolean Sudoku Solver (BSS) using only simple Boolean algebras. Use of Boolean algebra increases the execution speed of the Sudoku solver. Simulation results show that our method returns the solution of the Sudoku ...

Two Sudoku Rules in Conjunctive Normal Form