The Math Behind Sudoku

3. Counting Solutions

An interesting question to ask is how many ways can a 9 by 9 Sudoku grid be

filled so that it satisfies the One Rule? In other words, how many distinct Sudoku

solutions are there? We describe the method used to calculate this number by

Bertram Felgenhauer and Frazer Jarvis in early 2006.

To keep our language standard, we call the three rows of blocks the bands of

the grid and the three columns of blocks the stacks. A cell in the i

th

row and j

th

column is said to be in (i,j) position.