document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1080520>Question 1080520</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of a two digit number and the number obtained by reversing its digits is a square number. How many such numbers are there? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #694654 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=694654\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%288%29 ALIGN=MIDDLE  ALT=\"highlight%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > be the first digit, and let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > be the second digit.<BR>\n" );
document.write( "The value of the number is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10a%2Bb ALIGN=MIDDLE  ALT=\"10a%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The value of the number obtained by reversing its digits is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10b%2Ba ALIGN=MIDDLE  ALT=\"10b%2Ba\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Their sum is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10a%2Bb%2B10b%2Ba=11a%2B11b=11%28a%2Bb%29 ALIGN=MIDDLE  ALT=\"10a%2Bb%2B10b%2Ba=11a%2B11b=11%28a%2Bb%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "For that sum to be the square of an integer, it must be true that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bb=11 ALIGN=MIDDLE  ALT=\"a%2Bb=11\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "There are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > possible pastors of digits adding to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11 ALIGN=MIDDLE  ALT=\"11\"   DISABLED_style= \"max-width:90%; height:auto;\" > :<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2B9=11 ALIGN=MIDDLE  ALT=\"2%2B9=11\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2B8=11 ALIGN=MIDDLE  ALT=\"3%2B8=11\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2B7=11 ALIGN=MIDDLE  ALT=\"4%2B7=11\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2B6=11 ALIGN=MIDDLE  ALT=\"5%2B6=11\"   DISABLED_style= \"max-width:90%; height:auto;\" > .s<BR>\n" );
document.write( "Since we can make two 2-digit number out of each paiR<BR>\n" );
document.write( "by changing the other of the digits,<BR>\n" );
document.write( "there are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A4=8 ALIGN=MIDDLE  ALT=\"2%2A4=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > numbers that could be<BR>\n" );
document.write( "the original 2-digit number in the problem. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );