Analysis of a Sudoku variation using partially ordered sets and equivalence relations

Abstract

Sudoku is a popular game of logic, and there are many variations of the standard puzzle. We investigate a variation of Sudoku that uses inequalities between cells rather than numerical clues. We begin with an overview of the rules and strategies of the game. We then examine the solvability of an individual $m\times n$ block with the use of partially ordered sets, and combine $2\times 2$ blocks to form $4\times 4$ puzzles.