mathschallenge.net

Problem

A boy writes down the counting numbers from 1 to 20 in order and because each of the numbers from 10 to 20 contain two digits he notes that he has actually written down thirty-one digits in total.

1. If his list went from 1 to 1000 how many digits would he have written down?
2. If one-thousand digits were written down in total, how many complete numbers would have been written down?