My take is: The magnets are conductive and complete an electric circuit composed of the battery and a section of the coil (toroid) thereby forming a solenoid. The battery-magnet assembly is in the center of the solenoid. The magnetic field of the solenoid is maximum at the center and decreases towards the end. Move further away from the ends and the field decreases even faster. The north and south poles of the magnet is oriented so that the magnetic field of solenoid and of the magnets are oppositely oriented, and the solenoid field will tend to push the magnets away from the center. And hence the assembly moves away. Repeat. If the assembly is flipped over, it will still work, because the battery polarity will also be reversed and the solenoid will produce magnetic field in the other direction. However, if only the magnets are flipped over the battery, then I think the assembly will tend to be stuck at the center. Also, instead of flipping the magnet, if a different toroid, where the wire is wound the other way is used, it will fail. Am I right?