document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1176475>Question 1176475</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given that a total of 149 1's are used for all the page numbers in a book, at least how many pages are there in the book?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #803512 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=803512\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "There is no magic formula for working a problem like this.  You just need to count the 1's that are used in numbering the pages of a book.<br><BR>\n" );
document.write( "I will solve a similar problem using different numbers; then you can use the process to solve your problem.<br><BR>\n" );
document.write( "Find the number of pages in a book if a total of 172 3's are used.<br><BR>\n" );
document.write( "1-digit numbers: the digit 3 is used 1 time.<br><BR>\n" );
document.write( "2-digit numbers: the digit 3 is used 20 times -- 10 times as a tens digit and 10 times as a ones digit<br><BR>\n" );
document.write( "To this point we have used a total of 21 3's to number the pages.<br><BR>\n" );
document.write( "3-digit numbers 100-199: no 3's in the hundreds column; so again 20 3's.<br><BR>\n" );
document.write( "3-digit numbers 200-299: same as 100-199 -- 20 more 3's.<br><BR>\n" );
document.write( "To this point we have used 61 3's to number the pages; we need to use 111 more.<br><BR>\n" );
document.write( "3-digit numbers 300-399: To write all those page numbers, we would have the 20 3's in the tens and ones columns again, plus 100 3's in the hundreds column.  That's 120 more 3's; but we only have 111 left.<br><BR>\n" );
document.write( "So now we do some good old guessing and checking.  The page numbers 390-399 use 11 3's -- 10 in the hundreds column and 1 in the ones column.  11 off of the 120 it takes to write all the page numbers to 399 leaves us with a total of 109; add that to the 61 3's we used to write the page numbers 1-299 and we see that we have used 170 3's to write the page numbers from 1 to 389.<br><BR>\n" );
document.write( "So we need to use 2 more 3's; we will do that in writing the page numbers 390 and 391.<br><BR>\n" );
document.write( "So our answer is that the number of pages in the book is 391 if we use 172 3's to write all the page numbers.<br><BR>\n" );
document.write( "Now go through a similar process to solve your problem....<br><BR>\n" );
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