## Task A-1.5.

Marko drew a rectangle with dimensions $20 \times 15$ and divided it into unit squares with lines. How many squares are there in total on that picture?
## First Solution.

We count the squares based on their dimension, i.e., the length of the side:

squares with side length 1: $20 \cdot 15$

squares with side length 2: $19 \cdot 14$

squares with side length 3: $18 \cdot 13$

$\vdots \quad \vdots$

squares with side length 15: $6 \cdot 1$

(12 points*)

The total number of squares is:

$$
\begin{array}{rlr}
S & =20 \cdot 15+19 \cdot 14+18 \cdot 13+\cdots+7 \cdot 2+6 \cdot 1 & \text { (3 points) } \\
& =300+266+234+204+176+150+126+104+84+66+50+36+24+14+6 \\
& =1840 .
\end{array}
$$

* Note. If the number of squares with side length $d$ is determined for only a few values of $d$, a maximum of 5 points can be awarded, as follows: 1 point for $d=1, 2$ points for any other $d$, and 5 points for at least three different values of $d$.