If you walk into a bookstore, you're bound to find entire shelves made up entirely of books containing over 100 different Sudoku puzzles for the reader to solve. Over the past 10 years, Sudoku has become an internationally renowned puzzle game reaching the same amount, or even surpassing, in popularity as crosswords. In this article, I will explore how to determine how many fundamentally different completed Sudoku puzzles (known as Sudoku squares) exist. To do this, I will first give a brief history of the origin of Sudoku puzzles, then I will show how to determine how many Sudoku squares exist, which will lead me to determine how many existing Sudoku squares are fundamentally different from each other. others.Latin SquaresSudoku puzzles originate from Latin squares which have been studied by mathematicians for centuries. A Latin square of order n is a square with n rows and n columns where each row and column contains each of the n symbols appearing exactly once. Here are some examples below. Those who are fans of Sudoku puzzles will notice that a Sudoku puzzle is a 9x9 Latin square without the criteria of a 3x3 block. Counting Sudoku SquaresShidoku SquaresAt Barnes & Noble, there is an entire section full of Sudoku puzzles. They include books like Treacherous Sudoku, Pocket Sudoku, Killer Sudoku and Enslaved by Sudoku. With the amount of different Sudoku books out there, one question I had was how many different Sudoku squares can there be? Since there are so many restrictions on what constitutes a Sudoku square, we will first consider Shidoku squares since they will be easier to visualize. A Shidoku square is a 4x4 square which follows the same restrictions as South...... middle of paper ...... allowed them to use Burnside's lemma and they discovered (56(0)+48 (2)+4 (6)+6(8)+4(10)+1(12))/128=256/128=2, where 56 of the transformations corrected no squares and 1 transformation (the transformation d 'identity) corrected 12 squares. Thus, there are only two fundamentally different Shidoku squares. Now, there is also a less complicated way to determine how many fundamentally different Shidoku squares exist... p. 80, I'm not sure I want to take the time to explain that…. Sudoku Squares Earlier we determined that there are approximately 6.67 sextillion different valid Sudoku squares, our task is to use the six possible transformations (shown previously) and Burnside's Lemma to determine how many fundamentally different Sudoku squares exist. There are six basic transformations that can be applied to a Sudoku square, but we can combine multiple transformations to obtain a result.