Problem #WSP-000342

Problem

In the diagram below, there are nine discs - each is black on one side, and white on the other side. Two have black face-up right now. Your task is to remove all of the discs by making a series of the following moves. Each move includes choosing a black disc, flipping over its neighbours${}^{\ast }$ and removing that black disc. Discs are ‘neighbours’ if they’re adjacent at the beginning - removing a disc creates a gap, so that at later stages, a disc may have two, one or even zero neighbours left. $$\circ \circ \circ \bullet \circ \circ \circ \circ \bullet$$ Show that this task is impossible.