document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1207584>Question 1207584</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let $N$ be a positive integer.  The number $N$ has three digits when expressed in base $7$.  When the number $N$ is expressed in base $12$, it has the same three digits, in reverse order.  What is $N$?  (Express your answer in decimal.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #845542 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=845542\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "It appears that there is no solution.<br><BR>\n" );
document.write( "My work is shown below; perhaps another tutor will find an error in my work and find a solution to the problem.<br><BR>\n" );
document.write( "N = ABC base 12:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N=144A%2B12B%2BC ALIGN=MIDDLE  ALT=\"N=144A%2B12B%2BC\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "N = CBA base 7:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N=49C%2B7B%2BA ALIGN=MIDDLE  ALT=\"N=49C%2B7B%2BA\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Set the two expressions for N equal to each other and solve the resulting equation for one variable in terms of the other two.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=144A%2B12B%2BC=49C%2B7B%2BA ALIGN=MIDDLE  ALT=\"144A%2B12B%2BC=49C%2B7B%2BA\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=143A%2B5B=48C ALIGN=MIDDLE  ALT=\"143A%2B5B=48C\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5B=48C-143A ALIGN=MIDDLE  ALT=\"5B=48C-143A\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5B=%2845C-140A%29%2B%283C-3A%29 ALIGN=MIDDLE  ALT=\"5B=%2845C-140A%29%2B%283C-3A%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5B=%2845C-140A%29%2B3%28C-A%29 ALIGN=MIDDLE  ALT=\"5B=%2845C-140A%29%2B3%28C-A%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=%289C-28A%29%2B3%28C-A%29%2F5 ALIGN=MIDDLE  ALT=\"B=%289C-28A%29%2B3%28C-A%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "A, B, and C are positive integers less than 7, so in that last equation B, 9C, and 28A are all integers; that means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28C-A%29%2F5 ALIGN=MIDDLE  ALT=\"3%28C-A%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > must be an integer.<br><BR>\n" );
document.write( "That means C-A must be a multiple of 5; and since C and A are positive integers less than 7, C=6 and A=1.<br><BR>\n" );
document.write( "Then we have<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=9%286%29-28%281%29%2B3=29 ALIGN=MIDDLE  ALT=\"B=9%286%29-28%281%29%2B3=29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "But B has to be less than 6.<br><BR>\n" );
document.write( "So there is no solution.<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );