

Ask HN: How many combinations are possible in a 9X9 Sudoku matrix? - dmz

How many possible solutions can exist for 9X9 Sudoku puzzle?
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arvernus
Enumerating the Sudoku 9×9 grid solutions directly

The first approach taken historically to enumerate Sudoku solutions
(Enumerating possible Sudoku grids by Felgenhauer and Jarvis) was to analyze
the permutations of the top band used in valid solutions. Once the Band1
symmetries and equivalence classes for the partial grid solutions were
identified, the completions of the lower two bands were constructed and
counted for each equivalence class. Summing completions over the equivalence
classes, weighted by class size, gives the total number of solutions as
6,670,903,752,021,072,936,960 (6.67×1021). The value was subsequently
confirmed numerous times independently. The Algorithm details section (below)
describes the method.

([http://en.wikipedia.org/wiki/Mathematics_of_Sudoku#Enumerati...](http://en.wikipedia.org/wiki/Mathematics_of_Sudoku#Enumerating_all_possible_Sudoku_solutions))

