Problem 6.1. Find any solution to the puzzle

$$
\overline{A B}+A \cdot \overline{C C C}=247
$$

where $A, B, C$ are three different non-zero digits; the notation $\overline{A B}$ represents a two-digit number composed of the digits $A$ and $B$; the notation $\overline{C C C}$ represents a three-digit number consisting only of the digit $C$. Write the three-digit number $\overline{A B C}$ as your answer.
Answer: 251.

Solution. The number $\overline{C C C}$ is divisible by 111 and is less than 247, so $A \cdot \overline{C C C}$ is either 111 or 222. In the first case, we get that $\overline{A B}=247-111=136$, which is impossible. In the second case, $\overline{A B}=247-222=25$, that is, $A=2, B=5$, and therefore, $C=1$.