Find all natural numbers from 90 to 150 such that the digital sum of their digital sum is equal to 1.

(E. Semerádová)
The searched number is at most a three-digit number, so its digit sum is at most a two-digit number. For the digit sum of this number to be equal to 1, the digit sum of the searched number must be 1 or 10. The only natural number from 90 to 150 with a digit sum of 1 is the number 100. All natural numbers from 90 to 150 with a digit sum of 10 are 91, 109, 118, 127, 136, 145. The problem has a total of seven solutions:

$$
91, \quad 100, \quad 109, \quad 118, \quad 127, \quad 136, \quad 145 .
$$

Suggested evaluation. 1 point for identifying the possible digit sums of 1 and 10; distribute the remaining 4 points based on the number of solutions found (4 points for all 7 solutions, 3 points for 6-5 solutions, 2 points for 4-3 solutions, 1 point for 2-1 solutions).