Task B-4.2. A rectangular plate of dimensions $10 \times 9$ is divided by a grid of horizontal and vertical lines into squares of side length 1. How many squares are there in total on this plate?
Solution. Let's count the squares $1 \times 1$, then $2 \times 2, 3 \times 3, 4 \times 4, 5 \times 5, 6 \times 6, 7 \times 7$, $8 \times 8, 9 \times 9$ in sequence.

$$
\begin{array}{lllr}
\text { Squares of size } & 1 \times 1 & \text { there are } & 10 \cdot 9=90 \\
\text { Further, squares } & 2 \times 2 & \text { there are } & 9 \cdot 8=72 \\
& 3 \times 3 \quad \text { there are } & 8 \cdot 7=56 \\
& 4 \times 4 & \text { there are } & 7 \cdot 6=42 \\
& 5 \times 5 \quad \text { there are } & 6 \cdot 5=30 \\
& 6 \times 6 \quad \text { there are } & 5 \cdot 4=20 \\
& 7 \times 7 & \text { there are } & 4 \cdot 3=12 \\
& 8 \times 8 & \text { there are } & 3 \cdot 2=6 \\
& 9 \times 9 & \text { there are } & 2 \cdot 1=2
\end{array}
$$

In total, there are $2+6+12+20+30+42+56+72+90=330$ squares.