Okay, "guessing" is not the right word then. In a lot of sudokus, you can find the solution by eliminating possible numbers but in the harder ones you get stuck and need to think several steps ahead like you said. Does the P vs NP problem contain both "types"? I feel like the problem gets much...
If we suppose there is an algorithm for P vs NP, would it have to be able to find solutions where we now use trial and error? In harder Sudokus, for example, there are times when you have two or more possible numbers and need to guess whereafter you work the rest of the numbers through to see if...