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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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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