The general outline of the brute force method is to assign a different variable to each compound, set one variable as a constant (the "fifth" of the above problem), and solve for the other variables in terms of the constant. Finally, a value is assigned to the constant that eliminates denominators and minimizes the greatest common divisor of the coefficients. For problems such as the above example, the brute force method may not be necessary. However, although complicated, it can be applied to any problem.
