Problem

Source: 2022 South Russian Girls MO - Assara Juniors p6

Tags: combinatorics, Coloring



The cells of the $9 \times 9$ table are colored black and white. It turned out, that there were $k$ rows, in each of which there are more black cells than white ones white, and there were $k$ columns, each of which contained more than black. At what highest $ k$ is this possible?