## 7. Sequence of Numbers

The numbers are written without spaces, one after another

$123456789101112131415161718192021222324252627 \ldots$

Determine the digits at the 2019th, 2020th, and 2021st positions and write them in that order as a three-digit number.

## Result: $\quad 971$
## Solution.

There are 9 single-digit numbers, 90 two-digit numbers, and 900 three-digit numbers. For their writing, 9, 180, and 2700 digits are required, respectively.

The number containing the 2020th digit is a three-digit number. For writing all single-digit and two-digit numbers, a total of $9+180=189$ digits are needed, leaving 2020-189 = 1831 digits.

$1831 \div 3 = 610$ with a remainder of 1, so 610 three-digit numbers can be written with those 1831 digits, and one digit remains.

This means that the 2020th digit is located in the first position of the 611th three-digit number.

That number is $9+90+611=710$ (and the 2020th digit is 7).