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Question 929300: Can someone please help me with this problem?
Suppose that it takes 927 digits to number the pages of a book beginning with page 1 and ending with the last page of text. How many numbered pages are contained in this book? Your answer must include a method of solution and please state your answer in a sentence.
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! THE FIFTH-GRADER SOLUTION:
There are  pages with page number < 10,
and it takes only  digit/character to print each page number for those pages,
for a total of  digits/characters to number those pages.
There are  numbers less than  , so there will be
pages with one-digit or two-digit page numbers.
Nine  of those pages have one-digit numbers, but the remaining
 of those pages have two-digit page numbers.
As it takes  digits/characters to print the each page number for those pages,
 digits/characters will be used to number the pages with two-digit numbers.
So far, to number pages 1 through 99, we have used  digits/characters .
For most books, after page 99, all the other pages have 3-digit numbers,
and it takes  digits/characters to print the each page number for those pages.
If the book has  pages, there will be pages with one-digit or two-digit page numbers.
If  , the remaining  pages will have 3-digit page numbers, and we have  digits/characters left to print the 3-digit page numbers on those pages.
At 3 digits per page, we can number  such pages.
After that we will have numbered all  pages of the book.
TO SHOW OFF YOUR ALGEBRA SKILLS:
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