Sudoku Puzzle Games

Sudoku is a combinatorial, number-placement puzzle game based on logic, and its objective is to fill a 9x9 grid, in such way that each column, each row and each 3x3 boxes composing the bigger square, contains the digits 1-9 only one time. Euler is often mentioned as the source of the puzzle, maybe because his work related to Latin squares, but the modern version of the puzzle was invented by Howard Garns, an American architect, in 1979, and it was published in Dell Magazines. It became popular in 1986, when a Japanese puzzle company called Nikoli, brought it to the public with Sudoku name, and it became an international hit only in 2005.

Sudoku completed grids are nothing more than Latin squares, which have the property of no repeated values, in any of the 9 blocks of 3x3 cells. Dennis Berthier, in his book, "The Hidden Logic of Sudoku", proved that a first order formula doesn't mentions blocks, is valid for Sudoku, if and only if this order is valid for Latin Squares. The first calculation of the number of a classic Sudoku game solutions, with 9x9 grids, was posted on the USENET newsgroup in September 2003. There are quite a lot solution for only one grid:  6,670,903,752,021,072,936,960.

In the United States, Sudoku was published for the first time by Wayne Gold, in The Conway Daily Sun, in New Hampshire, in 2004. Now, this game is pretty popular, on PCs, websites and mobile devices. It comes with a lot of Linux distributions and versions for video game consoles have been already released, like Nintendo DS, PlayStation and GameBoy or Xbox. Just after 2 weeks after Apple launched its online App Store in 2008, July, there were already prepared 30 Sudoku games for iPhone and iPod Touch users. A very well known video game which includes Sudoku is Brain Age, which sold more than 8 million copies around the world. Nintendo released the Brain Age2 version, which brings 100 new Sudoku puzzles and activities.

This funny game has a strong link to mathematics, and especially with Latin squares (an N × N table which must be filled with n different symbols in such a manner that each symbol occurs only once in each row and in each column). This sort of puzzle can be solved with a variety of algorithms (backtracking, brute-force method, optimization/stochastic search, constraint programming and others).

Some Sudoku games seem to be very hard, and they can only be solved with more logical systems more complex than the human mind. Most of the players would categorize them as unsolvable, after trying many solving techniques. Computer programmers were interested in these cases more than the other players, and they tried to solve them and then generate more difficult puzzles.

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