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 and in the figure below are at the intersection of the two diagonals of the two parallelograms. The line is the line we need.
