Question 26
Every square of a grid with $m$ rows and $n$ columns is colored white or black, subject to the following two conditions:
a. Each row contains equally many white and black squares.
b. If a row meets a column in a black square, that row and that column have the same number of black squares; similarly, if a row meets a column in a white square, that row and that column have the same number of white squares.
Find all possible pairs $(m,n)$ for which such a coloring exists.
a. Each row contains equally many white and black squares.
b. If a row meets a column in a black square, that row and that column have the same number of black squares; similarly, if a row meets a column in a white square, that row and that column have the same number of white squares.
Find all possible pairs $(m,n)$ for which such a coloring exists.