When Dr. Cohen finally finished typing her treatise, 'The Sleeping Habits of Columbian Edible Ants,' she was rather suprised to notice that the number of digits she used to number its pages was exactly a multiple of the number of pages in the treatise itself. This substantial piece of work contains over 1,000 pages, but fewer than 10,000. Exactly how many pages does it contain?

Tabby Tom

1,107 pages (3,321 digits) Pages 1 to 9 use 9 digits Pages 10 to 99 use (90 x 2) or 180 digits Pages 100 to 999 use (900 x 3) or 2,700 digits Pages 1,000 to 1,107 use (108 x 4) or 432 digits. Total digits 3,321 or (3 x 1,107). Oct 30 02, 7:36 PM