document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=796205>Question 796205</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A two digit number is 18 less than the sum of the squares of its digits. How many such numbers are there? </SPAN>\n" );
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document.write( "A two digit number is 18 less than the sum of the squares of its digits. How many such numbers are there?\r<BR>\n" );
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document.write( "Let tens and units digits be T and U, respectively<BR>\n" );
document.write( "Then: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10T+%2B+U+=+T%5E2+%2B+U%5E2+-+18 ALIGN=MIDDLE  ALT=\"10T+%2B+U+=+T%5E2+%2B+U%5E2+-+18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T%5E2+-+10T+%2B+U%5E2+-+U+-+18+=+0 ALIGN=MIDDLE  ALT=\"T%5E2+-+10T+%2B+U%5E2+-+U+-+18+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since the number is 18 less than the sum of the squares of its digits, then its units digit is greater than its tens digit, or U > T.\r<BR>\n" );
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document.write( "Therefore, with 9 being the largest digit, we:\r<BR>\n" );
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document.write( "Let U = 9<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T%5E2+-+10T+%2B+U%5E2+-+U+-+18+=+0 ALIGN=MIDDLE  ALT=\"T%5E2+-+10T+%2B+U%5E2+-+U+-+18+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T%5E2+-+10T+%2B+81+-+9+-+18+=+0 ALIGN=MIDDLE  ALT=\"T%5E2+-+10T+%2B+81+-+9+-+18+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T%5E2+-+10T+%2B+54+=+0 ALIGN=MIDDLE  ALT=\"T%5E2+-+10T+%2B+54+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ----- T is NOT an INTEGER\r<BR>\n" );
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document.write( "Let U = 8<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T%5E2+-+10T+%2B+U%5E2+-+U+-+18+=+0 ALIGN=MIDDLE  ALT=\"T%5E2+-+10T+%2B+U%5E2+-+U+-+18+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T%5E2+-+10T+%2B+64+-+8+-+18+=+0 ALIGN=MIDDLE  ALT=\"T%5E2+-+10T+%2B+64+-+8+-+18+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T%5E2+-+10T+%2B+40+=+0 ALIGN=MIDDLE  ALT=\"T%5E2+-+10T+%2B+40+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ----- T is NOT an INTEGER\r<BR>\n" );
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document.write( "Let U = 7<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T%5E2+-+10T+%2B+U%5E2+-+U+-+18+=+0 ALIGN=MIDDLE  ALT=\"T%5E2+-+10T+%2B+U%5E2+-+U+-+18+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T%5E2+-+10T+%2B+49+-+7+-+18+=+0 ALIGN=MIDDLE  ALT=\"T%5E2+-+10T+%2B+49+-+7+-+18+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T%5E2+-+10T+%2B+24+=+0 ALIGN=MIDDLE  ALT=\"T%5E2+-+10T+%2B+24+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "T, or tens digit = 6 or 4\r<BR>\n" );
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document.write( "This means that the number could be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%2867%29 ALIGN=MIDDLE  ALT=\"highlight_green%2867%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%2847%29 ALIGN=MIDDLE  ALT=\"highlight_green%2847%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let U = 6<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T%5E2+-+10T+%2B+U%5E2+-+U+%96+18+=+0 ALIGN=MIDDLE  ALT=\"T%5E2+-+10T+%2B+U%5E2+-+U+%96+18+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T%5E2+-+10T+%2B+36+-+6+-+18+=+0 ALIGN=MIDDLE  ALT=\"T%5E2+-+10T+%2B+36+-+6+-+18+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T%5E2+-+10T+%2B+12+=+0 ALIGN=MIDDLE  ALT=\"T%5E2+-+10T+%2B+12+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ----- T is NOT an INTEGER\r<BR>\n" );
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document.write( "No need to go any further since T &#8800; U, and U > T \r<BR>\n" );
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document.write( "You can do the check!! \r<BR>\n" );
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document.write( "Send comments, “thank-yous,” and inquiries to “D” at MathMadEzy@aol.com. Further help is available, online or in-person, for a fee, obviously. \r<BR>\n" );
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