document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=489206>Question 489206</A>: <I><SPAN STYLE=\"word-break: break-all;\"> can the set {1,2,...,2010) be partitioned into classes A1 ,A2 ,..,An such each of the classes contains the same number of elements and the sum of elements in each classes are the same<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 #333596 by </B><A HREF=/tutors/aboutme.mpl?userid=chessace><B>chessace(471)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=chessace><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=chessace><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=333596\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Yes, if and only if n is a divisor of 2010: n=1,2,3,5,67.<BR>\n" );
document.write( "Because there are an even number in the entire set, any divisor n of 2010 will allow you to creat n subsets of equal size and with equal totals.<BR>\n" );
document.write( "Use the \"Gauss in grade school\" trick to ensure that all subsets total a multiple of 2011:<BR>\n" );
document.write( "A1 gets 1 and 2010, A2 gets 2 and 2009, etc., repeating A1 after An in this cycle.<BR>\n" );
document.write( "n=1 is a trivial case, but meets the requirements.<BR>\n" );
document.write( "Any n not a divisor will fail to have the same size sets.\r<BR>\n" );
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