Question

You are hand-numbering the pages of a report. If there are 238 numbered pages, how many digits will you write?

Answer 1

The numnered pages will have pages
1 through 9 with one digit each
10 through 99 with 2 digits each
100 through 238 with 3 digits each

Answer 2

Yeah, I figured that, but I'm stuck on the next parts. would the answer be 601 digits, 605 digits, or 606 digits then?

Answer 3

There are 9 pages from 1 to 9
How many pages from 10 to 99?
How many pages from 100 to 238?

Answer 4

Look at pages 10 through 99. Subtract 9 from each number, it's as if it were pages 1 through 90, which is 90 pages.

Answer 5

Now look at pages 100 through 238, subtract 99 from each number, so it's as if it were pages 1 through 139, so there are 139 pages.

Answer 6

But wouldn't there be 91 digits between 10 and 99, because you count 10?

Answer 7

I was counting numbers, not digits. Digits is the next step.

Answer 8

I mean't numbers, my bad. But wouldn't there still be 91 numbers between 10-99?

Answer 9

You have 9 1-digit pages, 90 2-digit pages, and 139 3-digit pages

Answer 10

So then the answer would be 606 digits?

Answer 11

There are 90 2-digit numbers from 10 to 99. Think of it this way. All numbers from 1 to 100 are obviously 100 numbers. How many of the 100 numbers are 2-digit numbers? 100 is a 3-digit number. 1 - 9 are 9 1-digit number, so 100 - 1 - 9 = 90 2-digit numbers.

Answer 12

Yes, 9 x 1 + 90 x 2 + 139 x 3 = 606

Answer 13

Thank you! :)

Answer 14

wlcm