2. 103 Use 94 large and small bricks, each with dimensions $4 \times 10 \times 19$, to stack into a tower 94 bricks high, where each brick can be placed to provide a height of 4, 10, or 19. If all 94 bricks are used, how many different heights can the tower be (height unit in inches)?
[Solution] Since
$$
10 \times 5=19 \times 2+4 \times 3 \text {, }
$$

this means that each of the 5 bricks can provide a height of 10, totaling a height of 50 for the tower, and even if none of the 5 bricks provide a height of 10, they can still provide a height of 50 for the tower. Therefore, we can assume that among the 94 bricks, the number of bricks providing a height of 10 is no more than 4.

Let $x$ be the number of bricks each providing a height of 19, $y$ be the number of bricks each providing a height of 10 ($0 \leqslant y \leqslant 4$), and $94-x-y$ be the number of bricks each providing a height of 4. Thus, the height of the tower is
$$
4(94-x-y)+19 x+10 y=376+15 x+6 y.
$$
By $x+y \leqslant 94$, we get $0 \leqslant x \leqslant 94-y$.
When $y=0$, $x$ has 95 possible values;
When $y=1$, $x$ has 94 possible values;
When $y=2$, $x$ has 93 possible values;
When $y=3$, $x$ has 92 possible values;
When $y=4$, $x$ has 91 possible values.

Therefore, the tower can have
$$
95+94+93+92+91=465 \text { (ways) }
$$

different heights.
Next, we prove that these 465 heights are all different.
If the ordered pairs $\left(x_{1}, y_{1}\right)$ and $\left(x_{2}, y_{2}\right)$ give the same height for the tower, then
$$
376+15 x_{1}+6 y_{1}=376+15 x_{2}+6 y_{2},
$$

which simplifies to
$$
\begin{array}{c}
6\left(y_{1}-y_{2}\right)=15\left(x_{2}-x_{1}\right), \\
2\left(y_{1}-y_{2}\right)=5\left(x_{2}-x_{1}\right) .
\end{array}
$$

This shows that $y_{1}-y_{2}$ is a multiple of 5. But $\left|y_{1}-y_{2}\right| \leqslant 4$, so $y_{1}-y_{2}=0$, which means $y_{1}=y_{2}$, and thus $x_{1}=x_{2}$.

This indicates that different ordered pairs must correspond to different heights, hence these 465 heights are all different.
In conclusion, a total of 465 different heights of towers can be built.