document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199769>Question 1199769</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The correct addition 13 + 24 + 43 + 44 = 102 looks strange because it is in another base. The base is </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #833735 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=833735\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Possibly the fastest way to solve the problem is by trying different bases and finding the one that works.  But you can get better practice in problem-solving skills by solving the problem using logical reasoning.<br><BR>\n" );
document.write( "(1) The sum of the units digits in base 10 is 14; since the last digit in the sum in the unknown base is 2, the unknown base must be an integer that is a divisor of 14-2 = 12.<BR>\n" );
document.write( "(2) The addition in base 10 gives the result 124; since the addition in the unknown base gives a sum 102 using smaller digits, the base is greater than 10.<br><BR>\n" );
document.write( "The only integer that satisfies both conditions is 12.<br><BR>\n" );
document.write( "ANSWER: 12<br><BR>\n" );
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