Sudoku: estratégias e Estrutura

Abstract

Often, any game or activity involving numbers is associated with mathematics. Sudoku, the principle is just an organization of numbers that follow certain rules. It is not required any previous mathematical knowledge to solve a Sudoku game. In this text we explore the mathematics contained in the game. Is done an association between a game of Sudoku and a system of linear equations, where each equation is the algebraic representation of the rules and initial conditions of the game is made. The goal is look to the Sudoku game as a mathematical problem and its possible results in detail, interpreting the article in The American Mathematical Monthly, titled Sudoku: Strategy vs. Structure of Provan, 2009. The rules, history and some solving strategies are described. Each of the equations is described in detail, exemplifying how they apply to the game. Throughout the text are proven theorems that involve the strategies used in a single block in the resolution of the game, and also discusses whether under what conditions the system associated equations is successful in solving the game. For demonstration of these theorems some independent subjects of the system of equations are used. Therefore, all results and / or settings required for such statements are described in a specific chapter of the text