8.3. 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 curious numbers exist in total: a) three-digit curious numbers?; b) four-digit curious numbers?
Answer. a) 30 numbers; b) 10 numbers. Solution. a) see the solution to problem 7.3.

b) Let $\overline{t x y z}$ be a curious four-digit number. Reasoning similarly to the solution of problem 7.3, we get that the number $A$ can equal 999, while the other two cases are impossible (since the numbers 3333 and 6666 are not divisible by 9). Thus, $A=9(111 x+11 y+z)=999$. From this, $x=1, y=z=0$. As a result, we have 10 curious numbers: $1000,1001, \ldots, 1009$.