  We establish symmetry results for two categories of overdetermined obstacle
problems: a Serrin-type problem and a two-phase problem under the
overdetermination that the interface serves as a level surface of the solution.
The first proof avoids the method of moving planes; instead, it leverages the
comparison principle and the fact that the solution of the obstacle problem is
superharmonic within its domain. The second proof utilizes a suitable version
of Serrin's method of moving planes.
