It all began with Leonard Euler, a mathematician from Switzerland who lived between 1707 and 1783. Only a year before his death he published an article about "a new kind of magical squares". Today we refer to these as Latin squares.
A Latin square consist of a grid that has an equal number of columns and rows. In each cell there should be a single symbol, most often a number. The total amount of different numbers allowed must not exceed the total number of rows (or columns, as they are just as many). Furthermore, the cells should be used in such a way that each symbol is displayed only once in each column and in each row.
A Sudoku puzzle is a special kind of Latin square consisting of nine rows and nine columns - 81 squares, in other words. And the idea is to fill these squares with the numbers 1 to 9. What separates the Sudoku puzzle from other Latin squares, is the rule regarding it's boxes - the grid is further split in nine smaller squares, so called boxes.
The special rule in the Sudoku puzzle is that each box also must contain all of the numbers 1 to 9, only once. The idea of the game is to arrive at the final solution, starting from a grid with pre-determined numbers already filled in.
According to the German mathematician Bertram Felgenhauer there are 6 670 903 752 021 072 936 960 different Sudoku puzzles possible. But many of these Sudoku puzzles are very similar to each other. Essentially, it doesn't make a difference of you switch places for a few of the numbers - switching places in all instances of digits one and two, for example. Furthermore, there is no change in the puzzle by changing the sequence of the first three rows in the grid. And there are many similar ways in wich the symbols can be moved around the grid, while the Sudoku puzzle still remains the same.
By calculating the number of unique puzzles possible instead, the number of possible Sudokus is significantly reduced. Frazer Jarvis and Ed Russel from Great Britain recently proved that there are 5 472 730 538 Sudoku puzzles that could be considered distinctly different.
Keeping in mind that each of these can be the result of thousands of different starting configurations, we can rest assured that we can keep playing our favorite little puzzle game for quite some time without running out of original Sudoku puzzles.
Charles Hawkins is the webmaster of Sudokuhints.Info, where you can find many articles about playing Sudoku as well as on the many Sudoku variations available.
Source: www.articlesbase.com
