Two parallelogram-shaped cakes are sitting at random on a counter. Describe how to split both into two regions with equal area with a single stroke of a knife, that is, by drawing a single line in the plane. The two cakes, incidentally, are completely different parallelograms.
Solution
The points A and B in the figure below are at the intersection of the two diagonals of the two parallelograms. The line AB is the line we need.
