Exhaustive Search -- from Wolfram MathWorld

For discrete problems in which no efficient solution method is known, it might be necessary to test each possibility sequentially in order to determine if it is the solution. Such exhaustive examination of all possibilities is known as exhaustive search, direct search, or the "brute force" method. Unless it turns out that NP-problems are equivalent to P-problems, which seems unlikely but has not yet been proved, NP-problems can only be solved by exhaustive search in the worst case.