Thread: Pages in a book - need to verify my solution

Hi All,

I have solved this problem below. But the required answer and my answer don't match. Please help me find the mistake in my solution.

The pages of a book are numbered as 1, 2, 3, .... It is found that 195 digits are used.

(a) How many pages are numbered with a single-digit number?

(b) How many pages are numbered with a two-digit number?

(c) How many pages are there altogether?

(a) I got single-digit numbers = 9

(b) I got, two-digit numbers = 99 - 9 = 90

(c) This is the part I need verified.



The required answer is 101, I am not sure how to get there. Can you help identify my mistake. Thanks for your help.

two issues here:

first:
The number of 2 digit pages is 90, not 45.

If there were only 45 2 digit numbers, the pages would go
1,2,3,4,5,6,7,8,9,10,.......58,100

which is not correct as there would be pages missing between 58 and 100.


second:
The number of digits in the 3 digit pages is
195 - (number of digits in 1 digit pages) - (number of digits in 2 digit pages)
=195 - 9 - 90*2
= 6

Thanks @SpringFan25.

I feel really stupid now. I see how I mixed up no. of pages and no. of digits used!

So the digits used are

And hence Total no of pages, .

Which was the required answer.