  We answer some questions concerning the so called sigma-game of Sutner. It is
played on a graph where each vertex has a lamp, the light of which is toggled
by pressing any vertex with an edge directed to the lamp.
  For example, we show that every configuration of lamps can be lit if and only
if the number of complete matchings in the graph is odd. In the special case of
an orthogonal grid one gets a criterion for whether the number of monomer-dimer
tilings of an m times n grid is odd or even.
