Problem 1. Let's call a number small if it is a 10-digit number and there does not exist a smaller 10-digit number with the same sum of digits. How many small numbers exist
Solution. Answer: 90.

It is clear that the sum of the digits of a 10-digit number can take any value from 1 to 90 inclusive. For each of the 90 possible sums of the digits, there is a unique smallest 10-digit number with such a sum of digits. Therefore, there are 90 small numbers.

## Criteria

One of the largest suitable criteria is used:

7 p. Any complete solution to the problem.

1 p. There is only the correct answer.