[ Decimal numeral system ]

Top student Polycarp has formed a huge number by writing down natural numbers from 1 to 500 in a row:

123...10111213...499500. Poor student Kolya erased the first 500 digits of this number. What do you think, with which digit does the remaining number start?

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Note: Kolya was erasing digits, while Polycarp was writing down numbers - single-digit, two-digit, and three-digit.

## Solution

Out of the 500 digits erased by Kolya, 9 digits will be used for single-digit numbers, leaving 491 digits. For two-digit numbers, $90 \times 2 = 180$ digits will be used, leaving 311 digits. From this number of digits, 103 three-digit numbers can be formed, with 2 digits left over from the 104th number. This means that the digit we are interested in is the 3rd digit of the 104th three-digit number. This number is 203, so the digit we are looking for is 3.

## Answer

3.