Common sense would suggest that all observed properties in a linear system would likely be linear. The response of a pendulum to an impulse can be computed, and for multiple impulses, the individual solutions can be superimposed to obtain the resultant solution. Qualitatively however, non-linear behavior can be readily observed. e.g. two impulses with the proper timing can (instead of creating twice the amplitude) bring the system to a stop. Non-linear properties can also be observed in optical interference patterns even though Maxwell's equations are completely linear. The energy patterns of individual sources do not superimpose. Thereby, non-linear features are also readily observed in optical systems that are governed by linear equations. This puzzle seems to have a simple but not-so-obvious solution that "not all of the equations governing the properties of these systems are linear." In particular, the energy equations are in general quadratic in the linear parameters so that system properties involving the energy are not required to exhibit linear behavior. In the case of the pendulum with impulses 180 degrees out of phase, the sinusoids cancel in a linear fashion, but the system's energy response is non-linear. In the case of the optical interference pattern, we actually have energy and photon conservation even though the energy patterns of two sources do not superimpose. Instead, the electric fields of the two sources superimpose in a perfectly linear fashion. Am posting this in case anyone else may have been stumped by this puzzle. Perhaps the solution is obvious to many, but some viewers may find it of interest.