You have nine brass rings, but three are actually gold. Can you pick these out using a balance scale three times at the most?
Similar to how you can determine the hight of a building with a barometer, simply take this scale to your local goldsmith and give him the scale as payment for classifying your rings for you. This solves the problem by "using" the balance only once.
Or, line 3 of the rings on a solid, stable surface. Lift the scale well above the elevation of the rings and "use" it by releasing it. The impact of the scale hitting the rings will dent them, however, the more malleable gold will be more damaged than the brass. Repeat twice more, by which time the scale is likely broken and not heavy enough to cause impact damage (finally an explaination as to why the scales have limited useability!) to determine the nature of the remaining 6 rings.
:)
Historical answer
