document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=28577>Question 28577</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Is the following 15 puzzle solvable or unsolvable?\r<BR>\n" );
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document.write( "2  1  3  4\r<BR>\n" );
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document.write( "5  8  7  6\r<BR>\n" );
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document.write( "9  10  12  11\r<BR>\n" );
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document.write( "15  13  14  *  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #26205 by </B><A HREF=/tutors/aboutme.mpl?userid=astromathman><B>astromathman(21)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=astromathman><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=astromathman><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=26205\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> It is not solvable.  It takes 7 swaps of adjacent pairs to \"solve\" it.  Since 7 is an odd number, it is not solvable.  If it took an even number of swaps, it would be solvable.<BR>\n" );
document.write( "Note:<BR>\n" );
document.write( "In the first row, swap 2 and 1.<BR>\n" );
document.write( "In the third row, swap 11 and 12.<BR>\n" );
document.write( "In the 4th row, 15,13,14 --> 13, 15, 14 --> 13,14,15 (2 swaps)<BR>\n" );
document.write( "In the second row, 5, 8, 7, 6 --> 5, 7, 8, 6 --> 5, 7, 6, 8 --> 5, 6, 7, 8 (3 swaps).<BR>\n" );
document.write( "That's 7 swaps altogether.\r<BR>\n" );
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document.write( "To try it out, go to http://www.javaonthebrain.com/java/puzz15/.  You can get everything down to a single pair out of order, but no further. </SPAN>\n" );
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