document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1133013>Question 1133013</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the greatest possible sum that can result from<BR>\n" );
document.write( "BAD+MAD+DAM if different letters represent different digits chosen from 1, 3, 8 and 9? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #750171 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=750171\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the sum will be BAD+ MAD + DAM.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the most significant digits have to be B, D, or M.<BR>\n" );
document.write( "the next most significant digit has to be A.<BR>\n" );
document.write( "the least significant digit will be D or M.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "B, D, or M will have to be some combination of 9, 8, and 3.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "in order for B, D, or M to be the most significant digit, than A has to be equal to 1.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the sum of the most significant digits will always be 2000 regardless of the value of B, D, or M.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the sum of the next most significant digits will always be 30 because the middle digit is always 1.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that leaves the sum of the least significant digits to be the deciding factor.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the least significant digit sum will be 2 * D + M.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if D = 9 and M = 8, this sum will be 26.<BR>\n" );
document.write( "if D = 8 and M = 9, this sum will be 25.<BR>\n" );
document.write( "if D = 3 and M = 9, this sum will be 15.<BR>\n" );
document.write( "if D = 3 and M = 8, this sum will be 14.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the highest sum of the least significant digit will be when D = 9 and M = 8.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since A is always equal to 1, that means that B must be equal to 3.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your numbers have to be B = 3, A = 1 M = 8, D = 9\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the sum is equal to BAD + MAD + DAM which is equal to 319 + 819 + 918 = 2056.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this was confirmed by an analysis using excel which calculated all the possible combinations and cam up with the maximum value of 2056 which occurred when B = 3, A = 1, M = 8, and D = 9.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "i will confess that the analysis using excel was performed first.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that told me that the maximum value for the sum had to be 2056.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the logic was developed after the analysis using excel.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "here's the results of the analysis using excel.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/011907.jpg\" alt=\"$$$\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );