24. The width of a rectangle is called the length of its shortest side *). In how many different ways can a rectangle of width 3 be cut out from a square sheet of paper consisting of 100 cells? (Cuts must be made only along the cell boundaries.)
24. Let's call the length of a rectangle the length of its longer side (the length of a square is equal to its width). Let's calculate the number of different rectangles of length $l$, where $l=4,5,6,7,8,9,10$. Such rectangles can be either horizontal or vertical, depending on whether their longer side is horizontal or vertical. The number of vertical rectangles of size $3 \times l$ is equal to the number of different positions that the top right cell of such a rectangle can occupy within the original square, i.e., 8 ( $11-l$ ) (Fig. 24, where the positions that the top right cell can occupy are marked with crosses if $l=5$ ).

The same number of horizontal rectangles $3 \times l$ also exists, so the total number of such rectangles is $16(11-l)$. Similarly, we find the number of different squares $3 \times 3$; it is equal to $8^{2}$. The total number of rectangles of width 3 is

$$
\begin{aligned}
& 16(11-4)+16(11-5)+\ldots+16(11-10)+8^{2}= \\
& \quad=16(1+2+\ldots+7)+8^{2}=16 \cdot \frac{7 \cdot 8}{2}+8^{2}=8^{2} \cdot 8=8^{3}
\end{aligned}
$$