If 1890 digits are used to number the pages in a volume, how many pages are there?

Question

To number the pages of a bulky volume the printer used 1890 digits. How many pages has the volume?

Answer 1

We have $9\cdot 1+90\cdot 2=189$ digits from first $99$ pages. We have $1890-189=1701$ digits remaining and therefore $1701:3=567$ pages with three digits. Hence, the volume has $99+567=666$ pages.