Skip to main content
← Back to archive

Problem #28 · August 24, 2026

Natural numbers

The pages of a book are numbered from 11 to 150150. How many digits in total were used to number the pages?
  1. A150150
  2. B339339
  3. C342342
  4. D343343
  5. E450450

WORKED EXAMPLE

Solution

Group the numbers by their number of digits: from 11 to 99 there are 99 single-digit numbers, using 99 digits; from 1010 to 9999 there are 9090 two-digit numbers, using 90⋅2=18090\cdot2 = 180 digits; from 100100 to 150150 there are 150−100+1=51150 - 100 + 1 = 51 three-digit numbers, using 51⋅3=15351\cdot3 = 153 digits. Total: 9+180+153=3429 + 180 + 153 = 342.
Solve today's problem