document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=282572>Question 282572</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Magic squares\r<BR>\n" );
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document.write( "___5__________8__________13______\r<BR>\n" );
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document.write( "____ _________ ___________0_______\r<BR>\n" );
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document.write( "____45_______  ___________ ________\r<BR>\n" );
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document.write( "Help fill in the missing numbers, we don't understand the spaces mean that a missing number? THis is all they gave us in a square?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #205197 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=205197\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "Typically, a Magic Square is an <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large n\ \times\ n\"> grid filled with integers such that the sum across each row, the sum down each column, and the sum of each major diagonal, are all equal.\r<BR>\n" );
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document.write( "In the square you have presented, the numbers that are already filled in make it impossible to create a Magic Square by the typical rules as I know them.\r<BR>\n" );
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document.write( "Note that the sum of numbers in the top row is 26.  That means that the sum of the numbers in all of the rows, all of the columns, and the two long diagonals must also be 26.\r<BR>\n" );
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document.write( "The first thing that I noticed is that the middle number in the left hand columm must be a negative number because the 5 and the 45 already sum to 50, hence to get back to 26, you need a -24.  The lower right corner has to be 13, and that makes the center number in the bottom row be -32.  That leaves the center number in the center row, which, given the -24 and 0 in the other cells of the center row must be 50 in order to arrive at -26.\r<BR>\n" );
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document.write( "That leaves us with a magic square that has all of the rows and all of the columns be the same sum, but the diagonals fail.\r<BR>\n" );
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document.write( "If your instructor did not intend you to include the diagonals, then I have given you the solution you need.  If the diagonals do need to be included, then the problem has no solution.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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