document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1046168>Question 1046168</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello, I'm new to these kind of questions so I have no idea where to start... The question is:<BR>\n" );
document.write( "Tom bought a notebook with 100 sheets and numbered its pages consecutively from 1 to 200. Jerry pulled out 43 sheets and added up all 86 page numbers written on both sides of each of the sheets. Can the sum be equal to 2016? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #661671 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=661671\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First of all, you must realize that, for ANY sheet of the notebook,<BR>\n" );
document.write( "the front sheet will always be numbered ODD (and so the back page will always <BR>\n" );
document.write( "be numbered even.)\r<BR>\n" );
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document.write( "Thus, the number pages of the sheets will form a sequence that looks like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=O%5B1%5D ALIGN=MIDDLE  ALT=\"O%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=O%5B1%5D%2B1 ALIGN=MIDDLE  ALT=\"O%5B1%5D%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=O%5B2%5D ALIGN=MIDDLE  ALT=\"O%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=O%5B2%5D%2B1 ALIGN=MIDDLE  ALT=\"O%5B2%5D%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=O%5B3%5D ALIGN=MIDDLE  ALT=\"O%5B3%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=O%5B3%5D%2B1 ALIGN=MIDDLE  ALT=\"O%5B3%5D%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >,..., <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=O%5B42%5D ALIGN=MIDDLE  ALT=\"O%5B42%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=O%5B42%5D%2B1 ALIGN=MIDDLE  ALT=\"O%5B42%5D%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=O%5B43%5D ALIGN=MIDDLE  ALT=\"O%5B43%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=O%5B43%5D%2B1 ALIGN=MIDDLE  ALT=\"O%5B43%5D%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >,\r<BR>\n" );
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document.write( "where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=O%5Bk%5D ALIGN=MIDDLE  ALT=\"O%5Bk%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > denotes the odd number paging of the front page of the kth sheet.\r<BR>\n" );
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document.write( "Suppose we sum all of these pagings.  The sum would be \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sum%282%2AO%5Bk%5D%2C+k=1%2C43%29%2B43 ALIGN=MIDDLE  ALT=\"sum%282%2AO%5Bk%5D%2C+k=1%2C43%29%2B43\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Letting this equal 2016, we get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sum%282%2AO%5Bk%5D%2C+k=1%2C43%29%2B43+=+2016 ALIGN=MIDDLE  ALT=\"sum%282%2AO%5Bk%5D%2C+k=1%2C43%29%2B43+=+2016\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "===> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sum%28O%5Bk%5D%2C+k=1%2C43%29=+1973 ALIGN=MIDDLE  ALT=\"2sum%28O%5Bk%5D%2C+k=1%2C43%29=+1973\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Contradiction.\r<BR>\n" );
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document.write( "Therefore the sum CANNOT be 2016.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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