Problem #PRU-5144

Problem

There are $12$ light bulbs placed on top of the numbers on a clock face. Initially, only the bulb at $12$ is on. We can choose any $6$ consecutive bulbs and change their state simultaneously, that is, if any were on, we turn them off, if any were off, we turn them on. Can we perform this operation multiple times so that in the end only the bulb at $11$ is on?