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 what you guessed is right. There is a distinction between problems where the solution is given by the process of elimination and problems where you have to guess. Does P vs NP concern the former only or also the latter? An answer would be very much appreciated!