document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1105054>Question 1105054</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How many different 5-digit PINs contain the sequence 12 (order matters)\r<BR>\n" );
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document.write( "12000 counts<BR>\n" );
document.write( "12121 counts<BR>\n" );
document.write( "13332 doesn't count </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #719898 by </B><A HREF=/tutors/aboutme.mpl?userid=math_helper><B>math_helper(2461)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_helper><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=math_helper><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=719898\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There are 4 patterns to worry about:\r<BR>\n" );
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document.write( "12xxx   —> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+10%5E3+ ALIGN=MIDDLE  ALT=\"+10%5E3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x12xx   —>  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+10%5E3+ ALIGN=MIDDLE  ALT=\"+10%5E3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "xx12x   —> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+10%5E3+-+10+ ALIGN=MIDDLE  ALT=\"+10%5E3+-+10+\"   DISABLED_style= \"max-width:90%; height:auto;\" >   <<< minus 10 for the 1212x pattern already counted <BR>\n" );
document.write( "xxx12   —>  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+10%5E3+-+10+-+10+ ALIGN=MIDDLE  ALT=\"+10%5E3+-+10+-+10+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  <<< minus 20 for 12x12, x1212, both already counted<BR>\n" );
document.write( " ——<BR>\n" );
document.write( "That's  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4x10%5E3+-+30+ ALIGN=MIDDLE  ALT=\"+4x10%5E3+-+30+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  = <b>3970</b> \r<BR>\n" );
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document.write( "——<BR>\n" );
document.write( "Check using a Perl one-liner:<BR>\n" );
document.write( " perl -e 'for ($i=0, $s=0; $i<100000; $i++) { if ($i =~ /12/) { $s++; } }; print \"$s\n\";'<BR>\n" );
document.write( "3970<BR>\n" );
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