document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=2252>Question 2252</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In the following figure:A  B  C<BR>\n" );
document.write( "                              D<BR>\n" );
document.write( "                              E   F  G<BR>\n" );
document.write( "                                     H<BR>\n" );
document.write( "                                     I<BR>\n" );
document.write( "Each of the digits 1, 2, 3, 4, 5, 6, 7, 8, and 9 is:<BR>\n" );
document.write( "a)Represented by a different letter in the figure above.<BR>\n" );
document.write( "b)Positioned in the figure above so that each of A + B + C,C + D +E,E + F + G, and G + H + I is equal to 13.<BR>\n" );
document.write( "Which digit does E represent?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #928 by </B><A HREF=/tutors/aboutme.mpl?userid=khwang><B>khwang(438)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=khwang><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=928\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Sol: By given condition,  we have<BR>\n" );
document.write( " A+B+C = 13...(1)<BR>\n" );
document.write( " C+D+E = 13...(2)<BR>\n" );
document.write( " E+F+G = 13...(3)<BR>\n" );
document.write( " G+H+I = 13...(4)<BR>\n" );
document.write( " Add up (1)+(2)+(3)+(4), we get <BR>\n" );
document.write( " 52=13*4 = A + B + C+ C + D + E+ E + F + G+ G + H + I = C+E+G+(A + B + C+ D +E + F + G + H + I)<BR>\n" );
document.write( "    = C+E+G+(1+2+ 3+ 4+ 5+ 6+ 7+ 8+ 9) = C+E+G+(1+9)*9/2 = C+E+G + 45<BR>\n" );
document.write( "  <BR>\n" );
document.write( " Hence,C+E+G = 52 - 45 = 7...(5)\r<BR>\n" );
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document.write( " By (5), we have E = 7-C-G <= 7-3 = 4 (since, the smallest C,G are 1 or 2) <BR>\n" );
document.write( " By (2)-(5)., we get D-G = 6, or D = G+6...(6) <BR>\n" );
document.write( "             Since D,G are between 1 and 9,<BR>\n" );
document.write( "             so D= 7, 8,or 9, and we have G=1,2 or 3\r<BR>\n" );
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document.write( " By (3)-(5)., we get F-C = 6, or F = C+6...(7) <BR>\n" );
document.write( "             Since F,C are between 1 and 9,<BR>\n" );
document.write( "             so F= 7, 8,or 9, and we have C=1,2 or 3\r<BR>\n" );
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document.write( " By (6) ,(7) & (5):<BR>\n" );
document.write( " Case(i) When G =1, D = G+6 =7, <BR>\n" );
document.write( "         and then C = 2, F = C+6=8, E = 7-C-G= 4<BR>\n" );
document.write( "        Or C = 3, F = 9, E = 3 (invalid,since the same C,E value)\r<BR>\n" );
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document.write( " Case(ii) When G =2, D = G+6= 8, <BR>\n" );
document.write( "           and then C = 1, F = C+6=7, E= 7-C-G=4<BR>\n" );
document.write( "         Or C = 3, F = 9, E = 2(invalid,since the same C,G value)\r<BR>\n" );
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document.write( " Case(iii) When G =3, D = G+6=9,<BR>\n" );
document.write( "        and then C = 1, F = C+6=7, E =7-C-G= 3(invalid,since the same E,G value)<BR>\n" );
document.write( "        Or C = 2, F = C+6=8, E=7-C-G = 2(invalid,since the same C,E value)\r<BR>\n" );
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document.write( " In these three possible cases of the values of G, we obtain that the only valid value of E is 4.\r<BR>\n" );
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document.write( "Kenny\r<BR>\n" );
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