Unicity Concepts for Sudoku

TL;DR

This paper explores the unicity of solutions in a generalized Sudoku framework using new concepts like constraint sets, permutations, unicity cells, and rectangles, providing a theoretical foundation for understanding solution uniqueness.

Contribution

It introduces a generalized approach to analyze Sudoku solution unicity through novel concepts and properties, extending beyond classical Sudoku constraints.

Findings

Unicity characterized by permutations, unicity cells, and rectangles.

Constraint sets generalize rows, columns, and blocks.

Illustrated with examples to demonstrate unicity concepts.

Abstract

This paper deals with a generalized Sudoku problem and investigates the unicity of a given solution. We introduce constraint sets, which is a generalization of the rows, columns and blocks of a classical Sudoku puzzle. The unicity property is characterized by three different properties. We describe unicity by permutations, by unicity cells and by rectangles. These terms are defined in this paper and are illustrated with examples. Throughout this paper we are not concerned with the existence of a solution.