Question 98
Each cell of a square grid $100 \times 100$ contains a positive integer. A Grid Rectangle is called *Good* if the sum of numbers in all its cells is divisible by $17$. By one move it is allowed to color all the cells of some good rectangle. It is not allowed to color a certain cell twine. Find the maximum $d$ such that is possible to color at least $d$ cells in Some moves. Each cell of the $100 \times 100$ square contains a certain natural number. The rectangle whose sides go along the grid lines will be called good if the sum of the numbers in all its cells is divided by $17$. It is allowed to simultaneously paint over all cells in some good rectangle. One cell must not be painted twice. At what largest $d$ can I paint over at least $d$ cells at any location of the numbers?