Editing Equation solving (section)

===Brute force, trial and error, inspired guess===
If the solution set of an equation is restricted to a finite set (as is the case for equations in [[modular arithmetic]], for example), or can be limited to a finite number of possibilities (as is the case with some [[Diophantine equation]]s), the solution set can be found by [[Brute-force search|brute force]], that is, by testing each of the possible values ([[candidate solutions]]). It may be the case, though, that the number of possibilities to be considered, although finite, is so huge that an [[exhaustive search]] is not practically feasible; this is, in fact, a requirement for strong [[encryption]] methods.

As with all kinds of [[problem solving]], [[trial and error]] may sometimes yield a solution, in particular where the form of the equation, or its similarity to another equation with a known solution, may lead to an "inspired guess" at the solution. If a guess, when tested, fails to be a solution, consideration of the way in which it fails may lead to a modified guess.