Question 39
In each cell of a board with $a$ rows and $b$ columns a $0$ or a $1$ is written so that the following conditions hold.
* If a row and a column intersect in a cell containing $0$, then they contain the same number of zeros.
* If a row and a column intersect in a cell containing $1$, then they contain the same number of ones.
Find all pairs $a, b$, with $a \le b$, for which this is possible.
* If a row and a column intersect in a cell containing $0$, then they contain the same number of zeros.
* If a row and a column intersect in a cell containing $1$, then they contain the same number of ones.
Find all pairs $a, b$, with $a \le b$, for which this is possible.