When solving hard combinatorial problems, Backtracking provides an exact solution by executing a systematic Depth-First Search (DFS). However, it does so blindly, relying entirely on hitting an unfeasible boundary before turning around.
In algorithm design, brute force or exhaustive search should not be used unless absolutely necessary[cite the Magic Square[cite 11]. The objective is to arrange the numbers such that the sum of each individual row, column, and corner-to-corner diagonal matches exactly[cite: 12].