Professor Erasmus claims that he is able to cut a square into 100 rectangles by making nine horizontal cuts and nine vertical cuts (parallel to the sides of the square), so that
- exactly 9 of the resulting 100 rectangles are squares, and
- no two of these 9 resulting squares have the same area.
The professor modestly calls this the "Professor-Erasmus-dissection-of-a-square". Has the professor once again made one of his mathematical blunders, or does such a dissection indeed exist?