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 #661672 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=661672\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Each sheet has two sides, with two consecutive page numbers:<BR>\n" );
document.write( "1 and 2, on the first sheet, 3 and 4, on the second sheet, and so on.<BR>\n" );
document.write( "The numbers on the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5Eth ALIGN=MIDDLE  ALT=\"n%5Eth\"   DISABLED_style= \"max-width:90%; height:auto;\" > sheet were<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2n-1 ALIGN=MIDDLE  ALT=\"2n-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > on the first side, and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2n ALIGN=MIDDLE  ALT=\"2n\"   DISABLED_style= \"max-width:90%; height:auto;\" > on the flip/back side.<BR>\n" );
document.write( "Adding both of those numbers, you get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282n-1%29%2B2n=4n-1 ALIGN=MIDDLE  ALT=\"%282n-1%29%2B2n=4n-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Let's say the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=43 ALIGN=MIDDLE  ALT=\"43\"   DISABLED_style= \"max-width:90%; height:auto;\" > sheets Jerry pulled out were sheets number<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5B1%5D ALIGN=MIDDLE  ALT=\"n%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5B2%5D ALIGN=MIDDLE  ALT=\"n%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5B3%5D ALIGN=MIDDLE  ALT=\"n%5B3%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > , ...., and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5B43%5D ALIGN=MIDDLE  ALT=\"n%5B43%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The sum of page numbers on those sheets is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284n%5B1%5D-1%29%2B%284n%5B2%5D-1%29+%2B%284n%5B3%5D-1%29+%2B%22...%22%2B%284n%5B43%5D-1%29+=+++4%28n%5B1%5D%2Bn%5B2%5D%2Bn%5B3%5D%2B%22...%22%2Bn%5B43%5D%29-43=4%28n%5B1%5D%2Bn%5B2%5D%2Bn%5B3%5D%2B%22...%22%2Bn%5B43%5D%29-44%2B1=4%28n%5B1%5D%2Bn%5B2%5D%2Bn%5B3%5D%2B%22...%22%2Bn%5B43%5D-11%29%2B1 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n%5B1%5D%2Bn%5B2%5D%2Bn%5B3%5D%2B%22...%22%2Bn%5B43%5D-11%29 ALIGN=MIDDLE  ALT=\"%28n%5B1%5D%2Bn%5B2%5D%2Bn%5B3%5D%2B%22...%22%2Bn%5B43%5D-11%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is definitely a positive integer,<BR>\n" );
document.write( "so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28n%5B1%5D%2Bn%5B2%5D%2Bn%5B3%5D%2B%22...%22%2Bn%5B43%5D-11%29 ALIGN=MIDDLE  ALT=\"4%28n%5B1%5D%2Bn%5B2%5D%2Bn%5B3%5D%2B%22...%22%2Bn%5B43%5D-11%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is definitely a multiple of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and the sum,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28n%5B1%5D%2Bn%5B2%5D%2Bn%5B3%5D%2B%22...%22%2Bn%5B43%5D-11%29%2B1 ALIGN=MIDDLE  ALT=\"4%28n%5B1%5D%2Bn%5B2%5D%2Bn%5B3%5D%2B%22...%22%2Bn%5B43%5D-11%29%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "could not be a multiple of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "It could be<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2A503%2B1=2012%2B1=2013 ALIGN=MIDDLE  ALT=\"4%2A503%2B1=2012%2B1=2013\"   DISABLED_style= \"max-width:90%; height:auto;\" > , or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2A504%2B1=2016%2B1=2017 ALIGN=MIDDLE  ALT=\"4%2A504%2B1=2016%2B1=2017\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "but it could never be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2A504=2016 ALIGN=MIDDLE  ALT=\"4%2A504=2016\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "(It could not be 2014 or 2015, either). </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );