There are types of problems that humans can solve a lot easier than computers. These are typically somewhat spatial in nature (for example, a traveling salesman, knapsack problem) and rely on patterns, both of which are domains humans are great at. Another name for this class of problems is optimization problems, with solutions that minimize or maximize a particular aspect (for example, a minimum distance or maximum value). A subset of this class is constraint satisfaction problems, where a solution has to conform to a set of rules while minimizing or maximizing another attribute.
The brute force approach that's used to create these solutions is an algorithmic class called backtracking, in which many small choices are recursively added together to form a solution. Fundamentally, this search for the optimal solution can run to find all possible combinations ...