document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=106472>Question 106472</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find i six digit number in wich the first digit is one less than the second, the secound one less than the third, the fourth digit is one less than the fifth, and the fifth one is one less than the last. the second digit equals the sum of the last three digits and the third digit equals the sum of the secound and fourth digit. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #77480 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=77480\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Call the digits d1, d2, d3, d4, d5, and d6\r<BR>\n" );
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document.write( "The relationships described are:\r<BR>\n" );
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document.write( "d1 = d2 - 1<BR>\n" );
document.write( "d2 = d3 - 1<BR>\n" );
document.write( "d4 = d5 - 1<BR>\n" );
document.write( "d5 = d6 - 1<BR>\n" );
document.write( "d2 = d4 + d5 + d6<BR>\n" );
document.write( "d3 = d2 + d4\r<BR>\n" );
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document.write( "Giving us 6 linear equations in 6 variables.\r<BR>\n" );
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document.write( "Rearrange each equation so that you have an expression set equal to zero\r<BR>\n" );
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document.write( "1) d1 - d2 + 1 = 0<BR>\n" );
document.write( "2) d2 - d3 + 1 = 0<BR>\n" );
document.write( "3) d2 - d4 - d5 - d6 = 0<BR>\n" );
document.write( "4) -d2 + d3 -d4 = 0<BR>\n" );
document.write( "5) d4 - d5 + 1 = 0<BR>\n" );
document.write( "6) d5 - d6 + 1 = 0\r<BR>\n" );
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document.write( "Add equation 4) to equation 2), resulting in\r<BR>\n" );
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document.write( "0d2 + 0d3 - d4 + 1 = 0, which reduces to<BR>\n" );
document.write( "d4 = 1\r<BR>\n" );
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document.write( "Substituting d4 in equation 5), d5 = 2<BR>\n" );
document.write( "Substituting d5 in equation 6), d6 = 3<BR>\n" );
document.write( "Substituting d4, d5, and d6 in equation 3), d2 = 6<BR>\n" );
document.write( "Substituting d2 in equation 1), d1 = 5<BR>\n" );
document.write( "Substituting d2 in equation 2), d3 = 7\r<BR>\n" );
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document.write( "Hence the number is 567123.\r<BR>\n" );
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document.write( "Check,\r<BR>\n" );
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document.write( "5 is one less than 6.<BR>\n" );
document.write( "6 is one less than 7.<BR>\n" );
document.write( "1 is one less than 2.<BR>\n" );
document.write( "2 is one less than 3.<BR>\n" );
document.write( "6 is equal to 1 + 2 + 3<BR>\n" );
document.write( "7 is equal to 6 + 1\r<BR>\n" );
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document.write( " </SPAN>\n" );
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