This is an example of a so-called brute force algorithm -- i.e. one which solves a problem by exhaustively enumerating all possible solutions and then successively testing whether any of them are correct.  Somewhat more precisely, a problem \(X\) is said to admit a brute force solution if there exists a feasibly decidable relation \(R_X\) and a family of uniformly defined finite sets \(S_x\) such that \(x \in X\) if and only if there exists a feasibly sized witness \(y \in S_x\) such that \(R_X(x,y)\). Such a \(y\) is often called a certificate for \(x\)’s membership in \(X\). The procedure of deciding \(x \in X\) by exhaustively searching through all of the certificates \(y_0, y_1, \ldots \in S_x\) and checking if \(R_X(x,y)\) holds at each step is known as a brute force search. For instance, the membership of a propositional formula \(\phi\) with atomic letters among \(P_0,\ldots, P_{n-1}\) in the problem \(\sc{SAT}\) can be established by searching through the set \(S_{\phi}\) of possible valuation functions of type \(v:\{0,\ldots,n-1\} \rightarrow \{0,1\}\), to determine if there exists \(v \in S_{\phi}\) such that \(\llbracket \phi \rrbracket_v = 1\). Note, however, that since there are \(2^n\) functions in \(S_{\phi}\), this yields only an exponential time decision algorithm.