Question 37
A rectangular field has $m\times n$ unit-square cells, in $m$ rows and $n$ columns. Sprinklers are placed inside some cells. A sprinkler waters its own cell, every cell sharing a side with it, and also the cells in the same column with exactly one intervening cell. Find the minimum number of sprinklers needed to water the whole field in the following cases:
a) $m=4$;
b) $m=3$.
a) $m=4$;
b) $m=3$.