Antônio needs to discover a 3-digit code with different digits $A, B$, and $C$. He knows that $B$ is greater than $A$, that $A$ is less than $C$, and also that the following equalities hold.

$$
\begin{aligned}
& \begin{array}{|l|l|}
\hline B & B \\
\hline A & A \\
\hline
\end{array}+\begin{array}{|l|l|l|l|}
\hline C & C \\
\hline
\end{array}=\begin{array}{|l|l|l|}
\hline 2 & 4 & 2 \\
\hline
\end{array}
\end{aligned}
$$

![](https://cdn.mathpix.com/cropped/2024_05_01_666a1aec7e447b0a6cbeg-019.jpg?height=60&width=483&top_left_y=1529&top_left_x=752)

What is the code that Antônio is looking for?
The only way to obtain $360=2^{3} \times 3^{2} \times 5$ as a product of three single-digit numbers is $360=9 \times 8 \times 5$. Since $A$ is the smallest of the three, $A=5$. Therefore, $B=8$ and $C=9$, or $B=9$ and $C=8$, both options giving $A A+B B+C C=$ $55+88+99=242$. Thus, we have two possibilities for the code $A B C$, namely 589 or 598.