Editing P versus NP problem (section)

== Example ==
Consider the following yes/no problem: given an incomplete [[Sudoku]] grid of size <math>n^2 \times n^2</math>, is there at least one legal solution where every row, column, and <math>n \times n</math> square contains the integers 1 through <math>n^2</math>? It is straightforward to verify "yes" instances of this generalized Sudoku problem given a candidate solution. However, it is not known whether there is a polynomial-time algorithm that can correctly answer "yes" or "no" to all instances of this problem. Therefore, generalized Sudoku is in NP (quickly verifiable), but may or may not be in P (quickly solvable). (It is necessary to consider a generalized version of Sudoku, as any fixed size Sudoku has only a finite number of possible grids.  In this case the problem is in P, as the answer can be found by table lookup.)