document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=175459>Question 175459</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In numbering the pages of a book, a printer uses 522 digits. How many numbered pages does the book have?<BR>\n" );
document.write( ": So this is what i tried:<BR>\n" );
document.write( "Ones: 9<BR>\n" );
document.write( "Tens: 90<BR>\n" );
document.write( "Hundreds: 900<BR>\n" );
document.write( "I just don't know what to do, please, please help! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #130541 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=130541\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i second the motion:<BR>\n" );
document.write( "HELP !!!!!<BR>\n" );
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document.write( "how you interpret this is extremely important.<BR>\n" );
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document.write( "assume that a digit is any number 0-9<BR>\n" );
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document.write( "a 1 digit number has a maximum of 9 pages.<BR>\n" );
document.write( "a 2 digit number has a maximum of 19 pages.<BR>\n" );
document.write( "a 3 digit number has a maximum of 29 pages.<BR>\n" );
document.write( "a 4 digit number has a maximum of 39 pages.<BR>\n" );
document.write( "a 5 digit number has a maximum of 49 pages.<BR>\n" );
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document.write( "is there a pattern?<BR>\n" );
document.write( "can we form an equation from this?<BR>\n" );
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document.write( "here's a pattern that i see.<BR>\n" );
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document.write( "let n = number of digits.<BR>\n" );
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document.write( "when n = 1, the maximum number of pages is 10^1 - 1 = 10 - 1 = 9<BR>\n" );
document.write( "when n = 2, the maximum number of pages is 10^2 - 1 = 100 - 1 = 99<BR>\n" );
document.write( "when n = 3, the maximum number of pages is 10^3 - 1 = 1000 - 1 = 999<BR>\n" );
document.write( ".....<BR>\n" );
document.write( "carry this out to n = 522, and the maximum number of pages would be:<BR>\n" );
document.write( "10^522 - 1 = a very big number.<BR>\n" );
document.write( "this number is so big my calculator won't handle it.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "your answer should be:<BR>\n" );
document.write( "the maximum number of pages is 10^522 - 1.<BR>\n" );
document.write( "you answer should also be:<BR>\n" );
document.write( "the minimum number of pages is 10^522 - 10<BR>\n" );
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document.write( "here's why i think the minimum number of pages is 10^522 - 10.<BR>\n" );
document.write( "take n = 3.<BR>\n" );
document.write( "the maximum number of pages is 10^3 - 1 = 1000 - 1 = 999<BR>\n" );
document.write( "the smallest number would be 990 using all 3 digits.<BR>\n" );
document.write( "990 is 10^3 - 10 = 1000 - 10 = 990.<BR>\n" );
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document.write( "go two steps higher just to see if this holds:<BR>\n" );
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document.write( "take n = 5<BR>\n" );
document.write( "the maximum number of pages is 10^5 - 1 = 100,000 - 1 = 99,999<BR>\n" );
document.write( "the minimum number of pages is 10^5 - 10 = 100,000 - 10 = 99,990<BR>\n" );
document.write( "you can't go higher than 99,999 with 5 digits.<BR>\n" );
document.write( "you can't go lower than 99,990 with 5 digits.<BR>\n" );
document.write( "answer looks good.<BR>\n" );
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document.write( "answer is:<BR>\n" );
document.write( "maximum number of pages is 10^n - 1<BR>\n" );
document.write( "minimum number of pages is 10^n - 10<BR>\n" );
document.write( "---<BR>\n" );
document.write( "a caveat:<BR>\n" );
document.write( "10^n works if n is > 1.<BR>\n" );
document.write( "take n = 2<BR>\n" );
document.write( "max = 100 - 1 = 99<BR>\n" );
document.write( "min = 100 - 10 = 90<BR>\n" );
document.write( "---<BR>\n" );
document.write( "take n = 1, however:<BR>\n" );
document.write( "max = 10 - 1 = 9<BR>\n" );
document.write( "min = 10 - 10 = 0<BR>\n" );
document.write( "---<BR>\n" );
document.write( "since the numbering of pages starts at 1, you need to qualify your statement as follows:<BR>\n" );
document.write( "if n = 1, the maximum number of pages is 9, and the minimum number of pages is 1.<BR>\n" );
document.write( "if n > 1, the maximum number of pages is 10^n - 1, and the minimum number of pages is 10^n - 10.<BR>\n" );
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document.write( "hope this helps.<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );