Obsessive Sudoku fans take heart: There is little likelihood you'll run out of the logic puzzles any time soon.
According to an article in American Scientist that describes some of the mathematics of Sudoku, the total number of possible puzzle solutions is 6,670,903,752,021,072,936,960, or about 7 times 10 to the 21st power.
Well, almost that many. If various forms of duplication are removed, such as mirror-image solutions or solutions in which all the 5s and 6s are interchanged, the number drops to a mere 3.5 trillion. However, a more complete elimination of duplicate results by the same researchers puts the number even lower at 5.5 billion.
For those with a deeper longing for analysis, the article also alludes to serious academic research on the subject, such as a paper from the University of California's David Eppstein describing solution methods. But don't expect easy pointers; one sample sentence from Eppstein's paper reads, "A placement of nine copies of the digit x can be viewed as a perfect matching in a graph in which the vertices are the rows and columns of the grid, and in which two vertices are connected by an edge when x can be placed in the cell shared by the row and column corresponding to those vertices."
Sudoku logic puzzles consist of a nine-by-nine grid that's subdivided into nine three-by-three subsections. To solve the puzzle, each digit from 1 through 9 must be placed in each subsection, vertical column and horizontal row. Some of the numbers are given in the initial puzzle, and solvers must deduce from their locations which numbers the empty cells contain.