Question 1
A cutting of an $8 \times 8$ chessboard into rectangles is called diversified if the following two conditions hold:
* Each rectangle contains the same number of black and white cells.
* No two rectangles have the same total number of cells.
Find the largest $n$ such that a diversified cutting into $n$ rectangles exists. (Ratko Višak)
* Each rectangle contains the same number of black and white cells.
* No two rectangles have the same total number of cells.
Find the largest $n$ such that a diversified cutting into $n$ rectangles exists. (Ratko Višak)