1. A natural number has a digit sum of 2013. The next number has a smaller digit sum and is not divisible by 4. What is the digit sum of the next natural number.
Answer: 2005.

Solution. The sum of the digits of the next number decreases only if it ends in nine.

It cannot end in two or more nines, as the next number would end in two zeros and be divisible by 4.

Therefore, the 9 is replaced by 0, but the tens digit increases by 1. The sum of the digits of the next number is 2013-9+1=2005.

## Grading Criteria.

Answer without justification: 0 points.

Failure to explain that there is only one nine: 4 points.