9.2 Find all natural numbers that, when added to the sum of their digits, give 2021.
Solution: Since the remainders of a number and the sum of its digits when divided by 9 coincide, and the number 2021 has a remainder of 5, the sought number $n$ gives a remainder of 7. Since $n<2999$, the sum of its digits is no more than 29 and has a remainder of 7 when divided by 9. Therefore, it is equal to 7, 16, or 25, from which $n=2014, 2005$ or 1996. Of these numbers, 2014 and 1996 are suitable, but 2005 is not.

An alternative solution is possible that does not consider the remainders when dividing by 9 but limits the number of variants of the number $n$ through an estimate of the sum of the digits.

Criteria:

- Proven that $n \equiv 7(\bmod 9)$ - 2 points;
- Both answers are given - 1 point;
- Shown that the sum of the digits does not exceed 29 or another reasonably small number - 2 points.
- If a large number of variants are used, they must be presented in the solution, otherwise, this part of the solution gets - 0 points.