Mary baked a rectangular cake. John secretly carved out a small rectangular piece, ate it and got away. The remaining cake has to be split evenly between Mary’s two kids. The cake is layered, and the kids want to be sure they both get the same amount of each layer.
How could this be done with only one cut through the cake?
Make a vertical cut that goes through the midpoints of the original cake, and the midpoint of the missing section.
Proof
Cutting a rectangle through its midpoint will always divide it in half. Thus each half in our divided cake will have half of the original cake with half of the missing section.
This makes the size of each slice exactly equal.