document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=263811>Question 263811</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The addition problem below has a unique solution.  Each of the  letters Q, W and Y represents a different non zero digit.  What is the product of Q, W and Y? \r<BR>\n" );
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document.write( "               Q W W<BR>\n" );
document.write( "              +W W Q<BR>\n" );
document.write( "            __________<BR>\n" );
document.write( "              Y Q W Y </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #194406 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=194406\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "Look at the sum of the 100s digits.  The largest Q and W can be is 8 and 9 in some order.  Depending on whether or not there was a carry from the previous column, the most Q + W + a possible carry can be is 18, and since the sum is YQ, Y must be 1.\r<BR>\n" );
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document.write( "So, now we have:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \ \ Q\,WW\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ +WWQ\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \ \overline{1\,QW\,1}\">\r<BR>\n" );
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document.write( "Q plus W cannot equal 1 because that would mean that one of them had to be zero and the problem says the letters are all non-zero and the other would have to be 1 which is already used by Y and the problem says they are all different.\r<BR>\n" );
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document.write( "Therefore Q plus W must be 11.\r<BR>\n" );
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document.write( "Q = 9 if and only if W = 2<BR>\n" );
document.write( "Q = 8 if and only if W = 3\r<BR>\n" );
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document.write( "and so on until we get to\r<BR>\n" );
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document.write( "Q = 2 if and only if W = 9\r<BR>\n" );
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document.write( "But W + W + 1 must either equal W or 1W so the only possibility is W = 9, so that W + W + 1 = 9 + 9 + 1 = 18.  Hence Q = 2.\r<BR>\n" );
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document.write( "Therefore:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \ \ \,299\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ +992\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \ \,\overline{1291}\">\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "</font> </SPAN>\n" );
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