document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=934615>Question 934615</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How many numbers less than 1 million do not contain the digit 2? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #567639 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=567639\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> ANSWER:<BR>\n" );
document.write( "Counting only positive integers (not counting zero),<BR>\n" );
document.write( "there are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%5E6-1=531441-1=highlight%28531440%29 ALIGN=MIDDLE  ALT=\"9%5E6-1=531441-1=highlight%28531440%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > numbers less than 1 million that do not contain the digit 2.<BR>\n" );
document.write( "If we count zero, then it is just <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=531441 ALIGN=MIDDLE  ALT=\"531441\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "EXPLANATION:<BR>\n" );
document.write( "Counting zero, numbers less than 1 million can be considered sequences of 6 digits,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=%22000%2C000%22 ALIGN=MIDDLE  ALT=\"0+=%22000%2C000%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1=%22000%2C000%22 ALIGN=MIDDLE  ALT=\"1=%22000%2C000%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > , ..... <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22999%2C999%22 ALIGN=MIDDLE  ALT=\"%22999%2C999%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "so there are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10 ALIGN=MIDDLE  ALT=\"10\"   DISABLED_style= \"max-width:90%; height:auto;\" > possible choices for each digit position,<BR>\n" );
document.write( "and as a consequence <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2A10%2A10%2A10%2A10%2A10=10%5E6=%221%2C000%2C000%22 ALIGN=MIDDLE  ALT=\"10%2A10%2A10%2A10%2A10%2A10=10%5E6=%221%2C000%2C000%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "If we do not count <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=%22000%2C000%22 ALIGN=MIDDLE  ALT=\"0+=%22000%2C000%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > , then there would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > less.<BR>\n" );
document.write( "If we cannot use the digit <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "there are only <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   DISABLED_style= \"max-width:90%; height:auto;\" > choices for each digit position,<BR>\n" );
document.write( "and we get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%5E6=531441 ALIGN=MIDDLE  ALT=\"9%5E6=531441\"   DISABLED_style= \"max-width:90%; height:auto;\" > 6-digit sequences made from the digits 0,1,3,4,5,6,7,8,9,<BR>\n" );
document.write( "including <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22000%2C000%22 ALIGN=MIDDLE  ALT=\"%22000%2C000%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > , which represents the number <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" > .\r<BR>\n" );
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document.write( " </SPAN>\n" );
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