document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1065991>Question 1065991</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Call an integer dangerous if no two of its digits are equal and no digit is 2. Call an integer sexy if all its digits are odd. How many four-digit integers are either sexy or dangerous? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #681164 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=681164\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The 1st digit must exclude 0 or 2, so<BR>\n" );
document.write( "there are 8 choices for the 1st digit<BR>\n" );
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document.write( "The 2nd 2nd digit excludes the 1st digit<BR>\n" );
document.write( "and 2, so there are 8 choices<BR>\n" );
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document.write( "The 3rd digit excludes 1st and 2nd digits<BR>\n" );
document.write( "and 2, so there are 7 choices<BR>\n" );
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document.write( "There are 6 choices for the 4th digit<BR>\n" );
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document.write( "There are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+8%2A8%2A7%2A6+=+2688+ ALIGN=MIDDLE  ALT=\"+8%2A8%2A7%2A6+=+2688+\"   DISABLED_style= \"max-width:90%; height:auto;\" >- dangerous numbers<BR>\n" );
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document.write( "So there are no overlaps with sexy integers<BR>\n" );
document.write( "count the number of dangerous integers <BR>\n" );
document.write( "that have all odd digits<BR>\n" );
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document.write( "5 choices for the 1st ( dangerous integer ) digit<BR>\n" );
document.write( "are odd<BR>\n" );
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document.write( "4 choices for the 2nd digit are odd<BR>\n" );
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document.write( "3 choices the the 3rd are odd<BR>\n" );
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document.write( "2 choices for the 4th are odd<BR>\n" );
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document.write( "There are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5%2A4%2A3%2A2+=+120+ ALIGN=MIDDLE  ALT=\"+5%2A4%2A3%2A2+=+120+\"   DISABLED_style= \"max-width:90%; height:auto;\" > dangerous numbers that are sexy<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2688+-+120+=+2568+ ALIGN=MIDDLE  ALT=\"+2688+-+120+=+2568+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "There are 2568 dangerous numbers that are NOT sexy<BR>\n" );
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document.write( "There are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5%2A5%2A5%2A5+=+625+ ALIGN=MIDDLE  ALT=\"+5%2A5%2A5%2A5+=+625+\"   DISABLED_style= \"max-width:90%; height:auto;\" > sexy numbers<BR>\n" );
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document.write( "There are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2568+%2B+625+=+3193+ ALIGN=MIDDLE  ALT=\"+2568+%2B+625+=+3193+\"   DISABLED_style= \"max-width:90%; height:auto;\" > 4 digit numbers<BR>\n" );
document.write( "that are EITHER sexy or dangerous<BR>\n" );
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document.write( "Definitely get a 2nd opinion on this!!!<BR>\n" );
document.write( "I could easily be missing something\r<BR>\n" );
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