Sudoku Facts
A Sudoku puzzle can have more than one solution, but in this case the kind of logical reasoning we described while discussing solving strategies may fall short. It turns out that for a Sudoku of rank n, at least n2-1 distinct symbols must be used for the puzzle to have a unique solution.
Number of Possible Sudokus
There are 6,670,903,752,021,072,936,960 possible solvable Sudoku grids that yield a unique result (that’s 6 sextillion, 670 quintillion, 903 quadrillion, 752 trillion, 21 billion, 72 million, 936 thousand, 960 in case you were wondering). That’s way more than the number of stars in the universe.
Mathematics and Algorithms
If P = NP, it is decidable. Because this states that there must be an algorithm for generating solutions in polynomial time. Well, an algorithm is a sequence of steps that solves a problem. With that definition (and in fact most definitions of algorithm) any computer program is also an algorithm. Every Euler problem can be solved with a computer program, so the answer is yes.
Unsolved Mathematical Problems
The remaining six unsolved problems are the Birch and Swinnerton-Dyer conjecture, Hodge conjecture, Navier–Stokes existence and smoothness, P versus NP problem, Riemann hypothesis, and Yang–Mills existence and mass gap.