A Necessary Solution Condition for Sudoku

TL;DR

This paper introduces a new mathematical model encompassing Sudoku, Latin Squares, and gerechte designs, providing a necessary condition for solutions based on integer equations and inequalities.

Contribution

It presents a novel discrete mathematical framework that unifies Sudoku and related combinatorial designs, deriving a necessary solution condition.

Findings

Derived a necessary condition for solutions of the generalized problem.

Illustrated the theoretical results with practical examples.

Abstract

We develop a new discrete mathematical model which includes the classical Sudoku puzzle, Latin Squares and gerechte designs. This problem is described by integer equations and a special type of inequality constraint. We consider solutions of this generalized problem and derive a necessary condition on these solutions. The results are illustrated with examples.