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?

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- Oct 11th 2009, 03:11 AMmytan1963Primary 5 math problem sum 2
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? - Oct 11th 2009, 03:19 AMMatt Westwood
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 $\displaystyle n$

So you have $\displaystyle 9 + 180 + 3n = 1359$.

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.