Thread: Primary 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?

Originally Posted by mytan1963

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 $\displaystyle n$

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.