Brute forcing is the method of completing a problem in the most straightforward way possible, through bashing calculations, and can actually sometimes be faster than a more creative approach, and is thus an important tool to have.
Given the problem "How many outfits can you create with thirteen hats and seven pairs of shoes?", a method involving brute force would be to list all 91 possibilities (although this would not be a smart time to use brute force).
Another method of brute force is the Greedy Algorithm. As an example, given two sets and how can we maximize the sum of ? We sort the sets such that they are in increasing or decreasing order; then, the maximal sum is . The "greedy" part is when we maximize the sum each step by taking the largest possible term to add.
See the Rearrangement Inequality for consequences of the example (and a more formal proof).