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If a book numbered starting with 1 and using 2004 digits then what is the number of...

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christiano-cr7 | Salutatorian

Posted July 7, 2013 at 5:52 AM via web

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If a book numbered starting with 1 and using 2004 digits then what is the number of pages in the book.

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jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted July 7, 2013 at 6:05 AM (Answer #1)

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If the number of pages in the book is n we can get the following.

When 1<=n<=9 then we have 9 digits.

When 10<=n<=99 then we have 9+2xx90 = 189 digits.

So definitely the number of pages is ,ore than 100.

Let us assume it is 100<=n<=999. If this assumption is correct we will get a answer for n<=999.

The number of digits of the book would be;

9+2xx90+3(n-99) = 2004

n = (2004-180-9)/3+99

n = 704

 

So the answer we got is less than 999. That means our assumption is OK.

 

So the answer is 704 pages.

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