9.6. On an infinite strip of paper, all natural numbers whose digits sum to 2018 are written in ascending order. What number is written in the 225th position?

(Method Commission)
Answer: $3 \underbrace{999 \ldots 99} 8$.

223 nines

Solution. Since $2018=224 \cdot 9+2$, the smallest number with a digit sum of 2018 will be $2 \underbrace{999 \ldots 99}_{224 \text { nines }}$. This number has 225 digits. Consider 225-digit numbers where the leading digit is a three, and the rest are nines, except for exactly one eight. There are exactly 224 such numbers (as many positions for the eight) and each of them has a digit sum of 2018. The largest among these numbers is $N=3 \underbrace{999 \ldots 99}_{223 \text { nines }} 8$. Since all other 225-digit numbers with a digit sum of 2018 will have a leading digit of at least four, they will be larger than the specified numbers, and thus $N$ will be the 225th number with a digit sum of 2018.

Comment. Only the correct answer without justification 3 points.

If the participant miscalculated and obtained an incorrect answer with correct reasoning - no more than 5 points.

The smallest number with a digit sum of 2018 was correctly found in the work, but there was no further progress -1 point.