SOLUTION: in order to number the pages of a book, the printer used 2,989 digets. how many pages did the book have?

Question 227271: in order to number the pages of a book, the printer used 2,989 digets. how many pages did the book have?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Pages 1 through 9 use 1 digit each, for a total of 9 digits, leaving 2,980 digits remaining. Pages 10 through 99 use 2 digits each: 90 pages times 2 digits per page is 180 digits, leaving 2800 digits remaining. Pages 100 through 999 each use 3 digits: 900 pages times 3 digits is 2700 digits, leaving 100 digits remaining. Each subsequent page uses 4 digits, so there are enough digits left to number 100 divided by 4 equals 25 additional pages, namely page 1000 through 1024. The book, presuming it had no additional un-numbered pages, has 1024 pages.

John

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