I have just come up with 2 new problems inspired by today's div2D 2194D - Table Cut and I think they are quite interesting so I hope to share them with you all.

Original Problem :

(refer to the original statement for more clarity)
" Given a table of size $$$n \cdot m$$$, where each cell contains either $$$0$$$ or $$$1$$$. The task is to divide it into two parts with a cut that goes from the top left corner to the bottom right corner. The cut lines can only go right or down.

$$$a$$$ = the number of ones in the left part of the table after the cut,
$$$b$$$ = the number of ones in the other part of the table.
Maximize the value of $$$a \cdot b$$$. "

New Problem 1:

$$$a$$$ = the number of ones s in the left part of the table after the cut,
$$$b$$$ = the number of zeros in the other part of the table.
Maximize the value of $$$a$$$ plus $$$b$$$.

New Problem 2 (Not yet solved):

$$$a$$$ = the number of ones in the left part of the table after the cut,
$$$b$$$ = the number of zeros in the other part of the table.
Maximize the value of $$$a \cdot b$$$.

Feel free to discuss the solutions of these problems in the comment section!