Recently, researchers at Rambus proposed a ring-oscillator example as a challenge problem for analog verification: they asked researchers to identify conditions that will ensure that the oscillator is free from lock-up. We present a solution to this challenge problem. Our approach is primarily pencil-and-paper analysis. We prove properties of the oscillator circuit, and then use numerical computation to determine parameter values for which correct operation is guaranteed. In addition to answering the challenge question, our approach uncovered anomalous behaviors that could cause the circuit to fail to oscillate but that would be hard to detect by standard, simulation-based, design practices.