document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1070474>Question 1070474</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A mathematician was forgetting his password. However he has great memory for anything numerical so hd created a password in the gorm of ABCDE  where A, B, C, D and E are digits. Use the clues belos to figure out the mathematicians password.\r<BR>\n" );
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document.write( "five digits are positive unique and none prime.<BR>\n" );
document.write( "even and odd digits alternate.B, C and D are square numbers. <BR>\n" );
document.write( "A+D=B </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #685569 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=685569\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   DISABLED_style= \"max-width:90%; height:auto;\" > positive digits.<BR>\n" );
document.write( "Of those, 2, 3,5,and 7 are prime.<BR>\n" );
document.write( "The other 5 are 1,4,6,8, and 9.<BR>\n" );
document.write( " <BR>\n" );
document.write( "Since even and odd digits alternate,<BR>\n" );
document.write( "and the 5 digits must be<BR>\n" );
document.write( "even digits 4, 6, and 8,<BR>\n" );
document.write( "and odd digits 1 and 9,<BR>\n" );
document.write( "the even digits must be A, C, and E,<BR>\n" );
document.write( "while B and D are 1 and 9.<BR>\n" );
document.write( "Since A+D=E, with E being a digit, D cannot be 9,<BR>\n" );
document.write( "so it has to be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28D=1%29 ALIGN=MIDDLE  ALT=\"highlight%28D=1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28B=9%29 ALIGN=MIDDLE  ALT=\"highlight%28B=9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2BD=B ALIGN=MIDDLE  ALT=\"A%2BD=B\"   DISABLED_style= \"max-width:90%; height:auto;\" > means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2B1=9 ALIGN=MIDDLE  ALT=\"A%2B1=9\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=9-1 ALIGN=MIDDLE  ALT=\"A=9-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28A=8%29 ALIGN=MIDDLE  ALT=\"highlight%28A=8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "Of the 9 available digits exactly 3 are square,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1=1%5E2 ALIGN=MIDDLE  ALT=\"1=1%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4=2%5E2 ALIGN=MIDDLE  ALT=\"4=2%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9=3%5E2 ALIGN=MIDDLE  ALT=\"9=3%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Those will be the middle digits, B, C, and D.<BR>\n" );
document.write( "Since<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=9 ALIGN=MIDDLE  ALT=\"B=9\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=1 ALIGN=MIDDLE  ALT=\"D=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > , it must be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28C=4%29 ALIGN=MIDDLE  ALT=\"highlight%28C=4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "By elimination,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28E=6%29 ALIGN=MIDDLE  ALT=\"highlight%28E=6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The 5-digit password is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28ABCDE=89416%29 ALIGN=MIDDLE  ALT=\"highlight%28ABCDE=89416%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );