32. Let $m$ be the smallest number of circles of radius 1 that can cover a convex polygon $M$, and $n$ be the largest number of circles of diameter 1 that can be placed such that no two circles intersect and all their centers belong to the polygon $M$. Which number is greater: $-m$ or $n$?
32. Consider $n$ non-intersecting circles of diameter 1, the centers of which belong to the polygon $M$. Replace each circle with a concentric circle of radius 1. If the circles obtained in this way do not cover some point $A$ of the polygon $M$, then this point will be at a distance of at least 1 from the centers of all circles; therefore, a circle of diameter 1 with center $A$ does not intersect any of the original circles of diameter 1, and it can be added to these circles, which, however, contradicts the definition of the number $n$. Therefore, the $n$ circles of radius 1 completely cover the polygon. And since $m$ is the smallest number of circles of radius 1 that can cover the polygon $M$, then

$$
m \leqslant n
$$