document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1147211>Question 1147211</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Sherlock made an elaborate code to remember the 10-digit combination to his locker.  This is the code he came up with:\r<BR>\n" );
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document.write( "A - K - B - J - C - H - D - G - E - F\r<BR>\n" );
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document.write( "Each letter stands for a different single digit number, from 0-9.\r<BR>\n" );
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document.write( "To find the combination, study the clues below to figure out what digit is represented by each letter.  When two letters are written together without an operation symbol, they represent a tens digit and a ones digit.\r<BR>\n" );
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document.write( "D + D + D = F<BR>\n" );
document.write( "H + H = B<BR>\n" );
document.write( "G + B +E = F + A +C<BR>\n" );
document.write( "J + A = CC<BR>\n" );
document.write( "F x D = KG (x means multiplied by)<BR>\n" );
document.write( "B / H = K (/ means divided by)<BR>\n" );
document.write( "D x H = CK<BR>\n" );
document.write( "A x H = KE<BR>\n" );
document.write( "J / D = K<BR>\n" );
document.write( "D      H (this is fractions, D over J and H over B)<BR>\n" );
document.write( "-   =  -<BR>\n" );
document.write( "J       B\r<BR>\n" );
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document.write( "What is the 10 digit combination to Sherlock's locker? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #768565 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=768565\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H+%2B+H+=+2H+=+B ALIGN=MIDDLE  ALT=\"H+%2B+H+=+2H+=+B\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H%2FB+=+1%2F2 ALIGN=MIDDLE  ALT=\"H%2FB+=+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%2FJ+=+1%2F2 ALIGN=MIDDLE  ALT=\"D%2FJ+=+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=J%2FD+=+2 ALIGN=MIDDLE  ALT=\"J%2FD+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Hence <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=K+=+2 ALIGN=MIDDLE  ALT=\"K+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "We therefore also have a bunch of doubling pairs: 1-2, 2-4, 3-6, 4-8. But <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=K=2 ALIGN=MIDDLE  ALT=\"K=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=J ALIGN=MIDDLE  ALT=\"J\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D ALIGN=MIDDLE  ALT=\"D\"   DISABLED_style= \"max-width:90%; height:auto;\" > are either 3-6 or 4-8. \r<BR>\n" );
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document.write( "Note that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=J ALIGN=MIDDLE  ALT=\"J\"   DISABLED_style= \"max-width:90%; height:auto;\" > &  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D ALIGN=MIDDLE  ALT=\"D\"   DISABLED_style= \"max-width:90%; height:auto;\" > are one set, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H ALIGN=MIDDLE  ALT=\"H\"   DISABLED_style= \"max-width:90%; height:auto;\" > & <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B ALIGN=MIDDLE  ALT=\"B\"   DISABLED_style= \"max-width:90%; height:auto;\" > are the other distinct set. \r<BR>\n" );
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document.write( "Further, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D ALIGN=MIDDLE  ALT=\"D\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F ALIGN=MIDDLE  ALT=\"F\"   DISABLED_style= \"max-width:90%; height:auto;\" > are a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tripled ALIGN=MIDDLE  ALT=\"tripled\"   DISABLED_style= \"max-width:90%; height:auto;\" > pair. \r<BR>\n" );
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document.write( "Note that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F+=+3D ALIGN=MIDDLE  ALT=\"F+=+3D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+D ALIGN=MIDDLE  ALT=\"+D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1,2,3. But from above, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D ALIGN=MIDDLE  ALT=\"D\"   DISABLED_style= \"max-width:90%; height:auto;\" >=3,4, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D+=+3 ALIGN=MIDDLE  ALT=\"D+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "Then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=J+=+6 ALIGN=MIDDLE  ALT=\"J+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F+=+9 ALIGN=MIDDLE  ALT=\"F+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Further, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=HB ALIGN=MIDDLE  ALT=\"HB\"   DISABLED_style= \"max-width:90%; height:auto;\" > must be the other double pair available, 4-8. Hence <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H+=+4 ALIGN=MIDDLE  ALT=\"H+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B+=+8 ALIGN=MIDDLE  ALT=\"B+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "Now, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F+%2A+D+=+9+%2A+3+=+27+=+KG ALIGN=MIDDLE  ALT=\"F+%2A+D+=+9+%2A+3+=+27+=+KG\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=G+=+7 ALIGN=MIDDLE  ALT=\"G+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=J+=+6 ALIGN=MIDDLE  ALT=\"J+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=J+%2B+A+=+CC ALIGN=MIDDLE  ALT=\"J+%2B+A+=+CC\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=J%2BA+%3C+16 ALIGN=MIDDLE  ALT=\"J%2BA+%3C+16\"   DISABLED_style= \"max-width:90%; height:auto;\" > so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=CC+=+11 ALIGN=MIDDLE  ALT=\"CC+=+11\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=+1 ALIGN=MIDDLE  ALT=\"C+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "Further, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+5 ALIGN=MIDDLE  ALT=\"A+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2A+H+=+KE ALIGN=MIDDLE  ALT=\"A%2A+H+=+KE\"   DISABLED_style= \"max-width:90%; height:auto;\" > => <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5+%2A+4+=+2E+=+20 ALIGN=MIDDLE  ALT=\"5+%2A+4+=+2E+=+20\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=E+=+0 ALIGN=MIDDLE  ALT=\"E+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "solution: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+-+K+-+B+-+J+-+C+-+H+-+D+-+G+-+E+-+F ALIGN=MIDDLE  ALT=\"A+-+K+-+B+-+J+-+C+-+H+-+D+-+G+-+E+-+F\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5-2-8-6-1-4-3-7-0-9 ALIGN=MIDDLE  ALT=\"5-2-8-6-1-4-3-7-0-9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );