Redundant Sudoku Rules

TL;DR

This paper demonstrates that in Sudoku, many of the all-different constraints are redundant and can be removed without changing the problem's meaning, with a maximum of six such constraints being redundant.

Contribution

It proves that many subsets of six all-different constraints are redundant in Sudoku, establishing a maximal redundancy size, and presents a conjecture for binary inequality constraints.

Findings

Many subsets of six all-different rules are redundant in Sudoku.

Six is the maximum number of redundant rules that can be removed.

A conjecture is proposed for binary inequality constraints redundancy.

Abstract

The rules of Sudoku are often specified using twenty seven \texttt{all\_different} constraints, referred to as the {\em big} \mrules. Using graphical proofs and exploratory logic programming, the following main and new result is obtained: many subsets of six of these big \mrules are redundant (i.e., they are entailed by the remaining twenty one \mrules), and six is maximal (i.e., removing more than six \mrules is not possible while maintaining equivalence). The corresponding result for binary inequality constraints, referred to as the {\em small} \mrules, is stated as a conjecture.