The Mathematics of Sudoku

A very large number of people are fascinated by Sudoku puzzles because the reasoning behind the correct solution can be very difficult, even if the rules are simple. Many teachers recommend Sudoku as a good way to develop logical reasoning, no matter how old they teach. The complexity of each puzzle can adapt to any age. That is why I want to explore and study the concept behind solving puzzles to make puzzles so attractive and addictive.

In this article, I will explain mathematical aspects included in Sudoku. There is no math to actually solve a Sudoku game, but more is how to use it from creators. Most reports will consider a 9 x 9 grid, but we will briefly describe other size grids, also called variants. Mathematicians questioned "How many unique solutions do Sudoku have?" Though there may be thousands of answers to ideas, understanding concepts behind Sudoku will learn completely new aspects.

There are many ways to enumerate possible Sudoku solutions. To enumerate all possible Sudoku solutions, if Sudoku is not the same, they differ from others. Therefore, if they do not like it, all solutions will be considered. In 2005 Felgenhauer and Jarvis became the first companies to directly enumerate Sudoku Grid Solutions. This method is to analyze the top row placement used in an efficient solution. Their understanding of the complexity of calculating the Latin square number made them understand how they should get answers with fewer calculations. Therefore, by using remarking, this can shorten the count.

The combination theory and replacement group theory are greatly related to Sudoku's analysis. For this reason, my aim is to investigate these theories and to understand how it applies to methods of enumerating Sudoku meshes. In particular, I will focus on Felgenhauer and Jarvis methods, list all possible Sudoku grids, and they use some mathematical concepts. In addition, we will clarify the importance of using latin side and its Sudoku. There are many constraints on when similar solutions, such as solutions of similar structures, symmetry, are considered different. Maintaining symmetry is called remarking with reordering, reflection, transposition, rotation. Bernside's lemma is essentially one of the methods for calculating the number of different solutions.