The act of figuring out how to solve the problem is itself an act of trial and error. And in many problems, the clever part is figuring out how to target your

The act of figuring out how to solve the problem is itself an act of trial and error. And in many problems, the clever part is figuring out how to target your trial and error. For instance, if you want to find the global minimum of some function on the integers, you might realize you can find the roots of the derivative and test only the neighboring integers. If you want to divide 144359305 by 241, you're going to start by guessing how many times 241 goes into 1443, and then multiply to check whether that's right. If you want to compute floor(29489238428^(1/3)) by hand, you're better off smartly guessing and checking than trying to figure out a digit-by-digit cube root algorithm on the spot.