7.3. A natural number is called curious if, after subtracting the sum of its digits from it, the result is a number consisting of identical digits. How many three-digit curious numbers exist?
Answer: 30 numbers. Solution: Let $\overline{x y z}$ be a curious three-digit number. Then the number

$$
A=\overline{x y z}-(x+y+z)=100 x+10 y+z-(x+y+z)=9(11 x+y)
$$

is divisible by 9 and consists of identical digits, and $100-27 \leq A \leq 999-1$. Thus, $A$ can be either 99, 333, or 666.

In the case of $A=99$, we have $11 x+y=11$, then $x=1, y=0, z$ - any digit, i.e., in this case, there are 10 curious numbers: $100,101, \ldots, 109$.

In the case of $A=333$, we get $11 x+y=37$, then we sequentially determine the digits: $x=3, y=4$, $z$ - any digit, i.e., in this case, there are also 10 curious numbers.

In the case of $A=666$, we have $11 x+y=74$, and then $x=6, y=8, z$ - any digit, again we have 10 curious numbers.