document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1096948>Question 1096948</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What's the sum of all the three-digits numbers I can form from digits 0-9 if<BR>\n" );
document.write( "REPITITION is PROHIBITED </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #711406 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=711406\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> THE SUM OF ALL THE DIGITS IS 9000, but I was solving the wrong problem.\r<BR>\n" );
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document.write( "If we could use zero for the first digit, we would have a<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2A9%2A8=720 ALIGN=MIDDLE  ALT=\"10%2A9%2A8=720\"   DISABLED_style= \"max-width:90%; height:auto;\" > 3-digit sequences with no repeated digits.<BR>\n" );
document.write( "Because each of the 10 digits would be equally likely in each position,<BR>\n" );
document.write( "and the average digit is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280%2B9%29%2F2=4.5 ALIGN=MIDDLE  ALT=\"%280%2B9%29%2F2=4.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "the sum of all the digits on those <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2A8%2A7 ALIGN=MIDDLE  ALT=\"9%2A8%2A7\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3+-+digit ALIGN=MIDDLE  ALT=\"3+-+digit\"   DISABLED_style= \"max-width:90%; height:auto;\" > sequences is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=720%2A3%2A4.5=9720 ALIGN=MIDDLE  ALT=\"720%2A3%2A4.5=9720\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Of those 3-digit sequences, the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2A8=72 ALIGN=MIDDLE  ALT=\"9%2A8=72\"   DISABLED_style= \"max-width:90%; height:auto;\" > that begin with zero do not count as 3-digit numbers.<BR>\n" );
document.write( "The sum of their digits is the sum of the last two (non-zero) digits.<BR>\n" );
document.write( "Those last two digits are from 1 to 9,with an average of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2B9%29%2F2=5 ALIGN=MIDDLE  ALT=\"%281%2B9%29%2F2=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and each of those digits appears with the same frequency.<BR>\n" );
document.write( "So, the sum of those digits is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=72%2A2%2A5=720 ALIGN=MIDDLE  ALT=\"72%2A2%2A5=720\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Subtracting that sum<BR>\n" );
document.write( "(the sum of digits of the 3-digit no-repeat sequences that are not valid 3-digit numbers)<BR>\n" );
document.write( "from the sum of all digits of all 3-digit no-repeat sequences,<BR>\n" );
document.write( "we get the answer as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9720-720=highlight%289000%29 ALIGN=MIDDLE  ALT=\"9720-720=highlight%289000%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
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