Question 38
Let $a$ and $b$ be positive integers. Suppose an $a \times b$ square grid is given and $N$ of the $ab$ square boxes of the grid are marked by $\checkmark$. It was possible to mark all of the $ab$ boxes by repeating the following procedure:
Procedure: If you find a row or a column of the boxes for which all but one of the boxes lying in it are marked, then mark its remaining box.
Express the minimum possible value of $N$ in terms of $a$ and $b$ for which this is possible.
Procedure: If you find a row or a column of the boxes for which all but one of the boxes lying in it are marked, then mark its remaining box.
Express the minimum possible value of $N$ in terms of $a$ and $b$ for which this is possible.