Problem 3. Decrypt the numerical riddle $\overline{A B B}+\overline{B B}=\overline{B B A}$, where different letters represent different digits, and the same letters represent the same digits.
Solution. If we write the numbers in the given equation in expanded form, we get

$$
\begin{aligned}
& 100 A+10 B+B+10 B+B=100 B+10 B+A \\
& 9 A=8 B
\end{aligned}
$$

However, $A$ and $B$ are digits, so from the last equation, it follows that $A=8$ and $B=9$, i.e., $899+99=998$.