This one is a straight arithmetics problem.
The first 9 pages of the book, (pages 1 through 9) need 9 digits to enumerate (one per page).
Next, getting into the double digits, we have 90 pages (10 thorugh 99), for a total of 180 digits.
It's easy to calculate that if the book had more than 1000 pages, it would need at least
900*100 + 90*2 + 9 = 2889
digits to enumerate. Since we are dealing with less digits, there are no pages with numbers over 999, and thus all the pages after page 99 have three digits in their number.
So, to calculate the number of three-digit pages, simply subtract 189 from 2775 and divide by three:
(2775 - 189) / 3 = 2586 / 3 = 862
To 862 pages over 100, add the 99 pages before 100 to get a total of 961 pages. |