document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=471259>Question 471259</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The integers 11 through 16 are written on the 6 sides on a cube. A triple of faces that meet at one vertex shows 11, 12, 13. Another triple of faces that meet at a vertex shows 12, 15, 16. None of the pairs of numbers on opposite sides sum to 27. Which number is written on the face opposite 13?\r<BR>\n" );
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document.write( "choose the answer and explain the reason to choose your response16<BR>\n" );
document.write( "The answer is not unique.<BR>\n" );
document.write( "15<BR>\n" );
document.write( "The configuration is impossible.<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 #323272 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20056)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><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=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=323272\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 13 is opposite 16.\r<BR>\n" );
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document.write( "Explanation:<BR>\n" );
document.write( "Imagine the cube being a cardboard box, and <BR>\n" );
document.write( "that we cut 7 of the edges and fold it out flat,<BR>\n" );
document.write( "like this.  The bottom face does not move.\r<BR>\n" );
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document.write( "Since 12 is common to the two given triples of faces that meet<BR>\n" );
document.write( "at one vertex, let's put 12 on the bottom.  Then we can <BR>\n" );
document.write( "arbitrarily pick two faces adjacent to the BOTTOM to put the<BR>\n" );
document.write( "11 and 13 in.  I chose to put 11 in the FRONT and 13 on the <BR>\n" );
document.write( "RIGHT.  Then the 15 and 16 have to go LEFT and BACK.  But which<BR>\n" );
document.write( "way?  Since no two opposite faces can have sum 27, we can only <BR>\n" );
document.write( "put the 15 on the BACK and 16 on the LEFT. \r<BR>\n" );
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document.write( "So we have the answer already. That 13 has to be opposite 16.\r<BR>\n" );
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document.write( "And that leaves 14 for the TOP.  The TOP and BOTTOM are<BR>\n" );
document.write( "opposite faces, The RIGHT and LEFT are opposite faces,<BR>\n" );
document.write( "and the FRONT and BACK are opposite faces, and none have sum 27. \r<BR>\n" );
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document.write( "Edwin</pre><BR>\n" );
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