Determine for how many natural numbers greater than 900 and less than 1001 the digital sum of the digital sum of their digital sum is equal to 1.

(E. Semerádová)

Hint. What is the largest digital sum of numbers from 900 to 1001?
Among the numbers 900 and 1001, the number with the greatest digit sum is 999, which is 27; we don't need to consider larger sums.

Among the numbers 1 and 27, the number with the greatest digit sum is 19, which is 10; we don't need to consider larger sums.

Among the numbers 1 and 10, the digit sum of 1 is only found in the numbers 1 and 10; we don't need to consider other numbers.

Now, working backwards, we can determine all solutions (the first column is 1, and in each subsequent column are the numbers whose digit sum equals the number in the previous column):

| 1 | 1 | 1 | 1000 |
| :---: | :---: | :---: | :---: |
|  |  | 10 | 901 |
|  |  |  | 910 |
|  | 10 | 19 | 919 |
|  |  |  | 928 |
|  |  |  | 937 |
|  |  |  | 946 |
|  |  |  | 955 |
|  |  |  | 964 |
|  |  |  | 973 |
|  |  |  | 982 |
|  |  |  | 991 |

There are a total of 12 numbers with the specified properties.