Introduction to the P vs NP Problem
The vast majority of computer scientists believe that P is not equal to NP. It is reasonable to believe so because finding polynomial solutions to NP-Complete problems has not been accomplished yet.
Sudoku as an NP Problem
The generalised Sudoku problem is an NP-complete problem that involves additional constraints beyond the typical Latin square requirements.
Consequences of Solving P=NP
If P=NP, all NP problems could be solved deterministically in polynomial time, leading to significant improvements in solving algorithmic challenges.
Example of P vs NP Problem
If any one NP-Complete problem can be solved in polynomial time, then every NP-Complete problem can be solved in polynomial time, including the famous Traveling Salesman problem.
Current State and Implications
Although one-way functions have not been formally proven to exist, most mathematicians believe in their existence, which could have profound implications on the P vs NP debate.