If numbering a book requires 2649 digits how many pages does it have?

And how do you get that answer?If numbering a book requires 2649 digits how many pages does it have?
919If numbering a book requires 2649 digits how many pages does it have?
pages 1 - 9 takes 9 digits


pages 10-99 takes 2 * 90 = 180 digits


pages 100 -999 takes 3 * 900 = 2700 digits





9 + 180 + 2700 = 2889 digits





2889 - 2649 = 240





so you need 240 less digits than 999 pages


240 / 3 = 80 pages





the book has 919 pages





check: 1-9 ==%26gt; 9 digits


10 - 99 ==%26gt; 180 digits


100 - 919 = 820 *3 = 2460 digits





2460 + 180 + 9 = 2649 check
2649 - 9 (pages 1-9)


2640 - 90*2 (pages 10-99)


2460 - 900*3 is less than zero, meaning that there are less than 1000 pages.


Therefore, 2460 / 3 = 820 three digit pages (100 - 919)





So there are 919 pages in total.
From 1 - 9 it takes 9 digits.


From 10 - 99 it takes 90 * 2 = 180 digits. (Because there are 90 digits from 10 - 99 inclusive)


Cumulative no. of digits = 189


From 100 - 999 it takes 900 * 3 = 2700 digits.


Cumulative no. of digits = 2889 %26gt;%26gt; That's a bit too much.


From 100 - 799 it takes 700 * 3 = 2100 digits.


Cumulative no. of digits = 2100 + 189 = 2289.


From 800 - 899 it takes 100 * 3 = 300 digits.


Cumulative no. of digits = 2289 + 300 = 2589 digits.


From 900 - 949 it takes 50 * 3 = 150 digits.


Cumulative no. of digits = 2589 + 150 = 2739 %26gt;%26gt; That's a bit too much.


From 900 - 919 it takes 20 * 3 = 60 digits.


Cumulative no. of digits = 2589 + 60 = 2649 digits %26gt;%26gt; BULLSEYE! WOOOHOOO!





So the book consists of 919 pages.





Check: From 1 to 9 it takes 9 digits.


From 10 to 99 it takes 90 * 2 = 180 digits.


From 100 - 919 it takes 820 * 3 = 2460 digits.


Adding gives 9 + 180 + 2460 = 2649 digits.





I hope that helps. :)





me07.



9(1) + 90(2) + 3n = 2649


3n = 2460


n = 820


So # of pages = 9+90+820 = 919

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