KöMaL 2009 K225

Little Pete is playing with six identical square sheets of plastic on the table. He lays a square on the table, then he lays the next one, always making sure that the newly laid square joins at least one of the previous ones along the full length of an edge. (Vertices always meet vertices.) Show that the perimeters of all those figures obtained that may form the net of a cube unfolded in the plane, is the same.