Joshua counted the number of digits of all the page numbers in an encyclopedia. He found that a total of 1359 digits were used.
How many pages were there in the book?
The way I'd do this would be to split it up into totals for the 1-digit pages, then the 2-digit pages, then the 3-digit pages etc.
So there are 9 1-digit pages: that's 9.
Then there are 90 2-digit pages: that's 90 x 2 = 180.
Then there are a possible 900 3-digit pages: that's 900 x 3 = 2700.
Whoops, that's way over. That means there's definitely less than 1000 pages here.
So you need to find a number of 3-digit pages that make the total you need. Call that number
So you have .
That looks quite easy. Don't forget n is the number of 3-digit pages - you have to add to that the number of 1 and 2 digit pages when you've finished.