How many pages does the book have?

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

Answer:

-From page #1 to page # 9, there are 9 pages

-From page #10 to page # 99, there are 90 pages. However, since each page number has 2 digits, there are 180 digits from page # 10 to page # 99

-From page #100 to page # 999, there are 900 pages. However, since each page number has 3 digits, there are 2700 digits from page # 100 to page # 999

Since there are 1629 digits, we know so far that number of pages is less than 900

Now, we need to find out how many digits there are for those pages greater than 99 or those pages with 3 digits

Since there are 180+9 = 189 digits for pages with less than 3 digits, we can subtract 189 from 1629 digits to find the number of pages with 3 digits
1629 − 189 = 1440

1440 represents the pages with 3 digits, so number of pages with 3 digits = 1440/3 = 480

Thus, total number of pages = 480 + 90 + 9 = 579 pages