Question: How many Sudoku boards are there?
A: A completed Sudoku grid is a special type of Latin square with the additional property of no repeated values in any partition of the 9×9 block into contiguous 3×3 blocks. The relationship between the two theories is now completely known, after Denis Berthier has proven in his recent book, "The Hidden Logic of Sudoku", that a first order formula that does not mention blocks (also called boxes or regions) is valid for Sudoku if and only if it is valid for Latin Squares (this property is trivially true for the axioms and it can be extended to any formula).
The first known calculation of the number of classic 9×9 Sudoku solution grids was posted on a USENET newsgroup rec.puzzles in September of 2003 and is:
A: A completed Sudoku grid is a special type of Latin square with the additional property of no repeated values in any partition of the 9×9 block into contiguous 3×3 blocks. The relationship between the two theories is now completely known, after Denis Berthier has proven in his recent book, "The Hidden Logic of Sudoku", that a first order formula that does not mention blocks (also called boxes or regions) is valid for Sudoku if and only if it is valid for Latin Squares (this property is trivially true for the axioms and it can be extended to any formula).
The first known calculation of the number of classic 9×9 Sudoku solution grids was posted on a USENET newsgroup rec.puzzles in September of 2003 and is:
A proof that does not use computers is not yet known. (Here is your chance to make your mark!) To get a feel for how Felgenhauer and Jarvis counted the 9 X 9 Sudoku boards, look at a run through a similar argument for 4 X 4 boards:
Click here. It is a PDF.
Click here. It is a PDF.
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