1. Find 10 consecutive natural numbers, the sum of all digits of which equals 145.
Solution. Note that among ten consecutive natural numbers, each digit from 0 to 9 appears exactly once in the units place. Therefore, the sum of their last digits is always 45, and we need to make up the sum of 100 using the other digits. This can be easily done by taking all numbers from the same decade such that the sum of all digits, except the last one, of each of them equals 10. This is exactly how the answer was obtained. There are infinitely many answers, and the one given consists of the smallest possible numbers.

Answer: all numbers from 190 to 199.