It takes 1629 digits to number the pages of a book. how many pages does the book have?

This is a queston of mathematics

1) The first 9 pages (from 1 to 9) takes 1 digit each page => 9 digits

2) From page 10 to 99, there are 90 pages and each takes 2 digits => 2*90 = 180 digits

3) Calculate how many digits more you need to reach 1629 digits = 1629 - 180 - 9 = 1440

4) Divide 1440 between 3, which is the number of digit for pages from 100 to 999: 1440 / 3 = 480 pages

5) Then the total number of pages is 9 + 90 + 480 = 579 pages

Check:

from 1 to 9 -> 9 digits
from 10 to 99 -> 90 pages -> 90 *2 = 180 digits
from 100 to 579 -> 480 pages -> 480*3 = 1440 digits

Total
9 + 90 + 480 = 579 pages
9 + 180 + 1440 = 1629 digits