3.4. A natural number $n$ is written with different digits, the sum of which is 22. What can the sum of the digits of the number $n-1$ be? Find all possible options.

Answer, option 1. 15 and 24 (two answers).

Answer, option 2. 18 and 27 (two answers).

Answer, option 3. 20 and 29 (two answers).

Answer, option 4. 21 and 30 (two answers).
Solution Option 1. If the number $n$ does not end in 0, then the sum of the digits of $n-1$ is 1 less than the sum of the digits of $n$, which means it is 15. If the number $n$ does end in 0, then it ends in only one zero (since all digits in the decimal representation of $n$ are different). Then, if the number $n$ has the decimal representation $n=\overline{\ldots c b a 0}$, the number $n-1$ has the decimal representation $n-1=\overline{\ldots c b(a-1) 9}$, so the sum of the digits of $n-1$ is 8 more than that of $n$, which means it is 24.

To complete the solution, it remains to provide examples confirming that both answers are indeed possible. For the answer 15, the number 97 works, and for the answer 24, the number 970 works.