2A. Determine all three-digit numbers with distinct digits that are divisible by any two-digit number obtained by removing one of its digits without changing the order of the remaining digits.
Solution. Let $\overline{a b c}$ be a number that satisfies the conditions of the problem. Then $a \neq b \neq c \neq a$ and $\frac{\overline{a b c}}{\overline{a b}}, \frac{\overline{a b c}}{\overline{b c}}, \frac{\overline{a b c}}{\overline{a c}}$ are integers. Since

$$
\frac{\overline{a b c}}{\overline{a b}}=\frac{\overline{a b 0}+c}{\overline{a b}}=10+\frac{c}{\overline{a b}}
$$

it follows that $\frac{c}{\overline{a b}}$ is an integer, which is possible only if $c=0$. Since

$$
\frac{\overline{a b 0}}{\overline{a 0}}=\frac{\overline{a b}}{a}=10+\frac{b}{a}
$$

it follows that $a$ is a divisor of $b$. According to this, $a \in\{1,2,3,4\}$. From

$$
\frac{\overline{a b 0}}{\overline{b 0}}=\frac{\overline{a b}}{b}=\frac{10 a}{b}+1
$$

it follows that $b$ is a divisor of $10 a$. From the previous discussion, the numbers that satisfy the conditions of the problem are: 120, 150, 240, 360, 480.