Kanunnikov A. L.

In a square sandbox, evenly covered with a layer of sand 1 unit high, Masha and Pasha made cakes using a cylindrical bucket 2 units high. All of Masha's cakes turned out well, while Pasha's cakes crumbled and turned into cones of the same height. In the end, all the sand went into the cakes, which were placed on the bottom of the sandbox separately from each other. Whose cakes were there more of in the sandbox: Masha's or Pasha's?
Let there be $m$ Masha's and $n$ Pasha's kuliches in the sandbox. Denote by $S$ the area of the base of the bucket. Since all kuliches have the same heights and volumes, the area of the base of each conical kulich is $3 S$ (from the volume formulas for a cylinder and a cone).

The area of the base of the sandbox, on the one hand, is numerically equal to the volume of all the sand, i.e., the total volume $2 S(m+n)$ of all the kuliches, and on the other hand, is greater than the total area $S m + 3 S n$ of the bases of the kuliches, since these bases do not intersect and, being circles, cannot cover the entire square base of the sandbox. Therefore, $2 S(m+n) > S m + 3 S n$, from which it follows that $m > n$.

## Problem