Given a cake(cuboid) with a rectangular piece cut from it(any size or orientation), how would you divide the cake into two equal halves by a single cut of knife.

Solution #1: Consider a plane perpendicular to the cake and passing through the center of the cake. Now, no matter at what angle you keep this plane at, it will divide the cake in two equal halves. So, the point is, a perpendicular plane passing through the center of a cuboid will always divide it into two equal halves. Now, if we connect centers of cake and rectangular piece and run our knife through that line we will cut both of them in two equal halves giving us two equal halves of cake.