Question

To number the pages of a book, 2022 digits are used. How many pages are in the book?

Answer 1

710

Explanation:

Numeration of pages goes from 1.

9 pages with 1-digit numbers, from 1 to 9.

90 pages with 2-digit numbers, from 10 to 99.

So, 2*90 + 9 = 189 digits are just used to numerate 9 + 90 = 99 pages.

The rest of numbers are 3-digit.

`((2022-189))/(3)` = 611 pages with 3-digit numbers.

Total pages = 9 + 90 + 611 = 710.