2. Can the number 2020 be represented as the sum of 99 natural numbers with the same digit sum?
Solution. Each addend has the same sum of digits, so their remainders when divided by 3 are the same (the sum of the digits of a number gives the same remainder when divided by 3 (and 9) as the number itself). The sum of 99 identical remainders is divisible by 3, which means the sum of any 99 natural numbers with the same sum of digits is divisible by 3. But the number 2020 is not divisible by 3. Answer: no.

Comment. Similarly, we can reason about the remainders when divided by 9.