Given a rectangular (cuboidal for the puritans) cake with a rectangular piece removed (any size or orientation), how would you cut the remainder of the cake into two equal halves with one straight cut of a knife ?

 The cut (plane) should pass through the center of the two rectangles: the outer cake and the inner hollow area. Since any plane passing through the center of the cuboid will divide the volume in two halves, both the cake and hollow area are divided into two equal halves.