Problem 1. Vasya thought of a two-digit number, then added the digit 1 to the left of it, and the digit 8 to the right, which increased the number by 28 times. What number could Vasya have thought of? (Find all options and prove that there are no others.)
Answer: 56.

Solution. Let Vasya have thought of the number $n$. When the digit 8 is appended to the right, it turns into the number $10 n+8$, and when the digit 1 is appended to the left, it increases by 1000, therefore

$$
\begin{gathered}
10 n+1008=28 n \\
18 n=1008 \\
n=56
\end{gathered}
$$

## Criteria

4 6. A complete and justified solution is provided.

In the absence of a correct solution, the highest applicable criterion from those listed below is used:

3 p. The equation is correctly set up, but an arithmetic error is made in solving it.

2 6. The correct answer is provided, but there is no justification.

06. The problem is not solved or is solved incorrectly.