document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=925269>Question 925269</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Drew purchased a used 50 page book. The book, in which left-hand pages contained even page #s and the right-hand pages contained odd page #s, did not contain all 50 pages.  The sum of the page #s on the pages that Drew's book did contain was 1242. What is the greatest page # that could be on a page missing from Drew's book? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #561608 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=561608\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In all books I have ever had, left-hand pages contained even page #s and the right-hand pages contained odd page #s. That sounds normal to me.<BR>\n" );
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document.write( "If one page is missing, the page on the reverse must be missing too.<BR>\n" );
document.write( "For example, if page 1 is missing, page 2, which is the other side must also be missing.<BR>\n" );
document.write( "So, missing pages must come in pairs: one odd numbered (right page), with number <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N ALIGN=MIDDLE  ALT=\"N\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and the even numbered page with the next page number, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N%2B1 ALIGN=MIDDLE  ALT=\"N%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "If just one such set of 2 pages is missing, the sum of their numbers will be<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N++%2B+%28N%2B1%29+=+2N+%2B+1 ALIGN=MIDDLE  ALT=\"N++%2B+%28N%2B1%29+=+2N+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
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document.write( "The numbers on all 50 pages add up to<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2B50%29%2A50%2F2=1275 ALIGN=MIDDLE  ALT=\"%281%2B50%29%2A50%2F2=1275\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The sum of numbers on the missing pages will be<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1275-1242=33 ALIGN=MIDDLE  ALT=\"1275-1242=33\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Could that be just 2 pages, an <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=odd ALIGN=MIDDLE  ALT=\"odd\"   DISABLED_style= \"max-width:90%; height:auto;\" > page and the next page?<BR>\n" );
document.write( "I don't think so, and I can explain why it cannot be so.<BR>\n" );
document.write( "If the pages missing were page <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N ALIGN=MIDDLE  ALT=\"N\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and page <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N%2B1 ALIGN=MIDDLE  ALT=\"N%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2N%2B1=33 ALIGN=MIDDLE  ALT=\"2N%2B1=33\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2N=33-1 ALIGN=MIDDLE  ALT=\"2N=33-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2N=32 ALIGN=MIDDLE  ALT=\"2N=32\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N=16 ALIGN=MIDDLE  ALT=\"N=16\"   DISABLED_style= \"max-width:90%; height:auto;\" > and that does not work, because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16 ALIGN=MIDDLE  ALT=\"16\"   DISABLED_style= \"max-width:90%; height:auto;\" > is not odd.<BR>\n" );
document.write( "The book cannot be missing just page 16 and page 17, because the reverse of page 16 is page 15 and the reverse of page 17 is page 18.<BR>\n" );
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document.write( "Since the sum of the numbers of the missing pages is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=33 ALIGN=MIDDLE  ALT=\"33\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is odd,<BR>\n" );
document.write( "and it cannot be the sum of the numbers of 1 pair of consecutive pages,<BR>\n" );
document.write( "it must be the sum of the numbers of 3 pairs of consecutive pages,<BR>\n" );
document.write( "because the sum of 2 pairs of consecutive pages would be even.<BR>\n" );
document.write( "Making the numbers in 2 of the 3 pairs as small as possible would make the numbers in the third pair as large as possible.<BR>\n" );
document.write( "The smallest 4 numbers are 1, 2, 3, and 4, and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2B2%2B3%2B4=10 ALIGN=MIDDLE  ALT=\"1%2B2%2B3%2B4=10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The sum of the third pair would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=33-10=23 ALIGN=MIDDLE  ALT=\"33-10=23\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2N%2B1=23 ALIGN=MIDDLE  ALT=\"2N%2B1=23\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2N=23-1 ALIGN=MIDDLE  ALT=\"2N=23-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2N=22 ALIGN=MIDDLE  ALT=\"2N=22\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N=11 ALIGN=MIDDLE  ALT=\"N=11\"   DISABLED_style= \"max-width:90%; height:auto;\" > gives us an odd first page.<BR>\n" );
document.write( "The reverse has the number <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N%2B1=highlight%2812%29 ALIGN=MIDDLE  ALT=\"N%2B1=highlight%2812%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and that would be the greatest page number that could be on a page missing from Drew's book.\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );