document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1210232>Question 1210232</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Recall that a partition of a positive integer n means a way of writing n as the sum of some positive integers, where the order of the parts does not matter.  For example, there are five partitions of 4:\r<BR>\n" );
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document.write( "4\r<BR>\n" );
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document.write( "3 + 1\r<BR>\n" );
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document.write( "2 + 2\r<BR>\n" );
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document.write( "2 + 1 + 1\r<BR>\n" );
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document.write( "1 + 1 + 1 + 1\r<BR>\n" );
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document.write( "How many partitions of 17 are there that have at least three parts, such that the largest, second-largest, third-largest, and fourth-largest parts are respectively greater than or equal to 4, 3, 2, and 1?\r<BR>\n" );
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document.write( "The partition 17 = 7 + 4 + 3 + 2 + 1 is one such partition.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #851943 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52781)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=851943\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .\r<BR>\n" );
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document.write( "As I read this problem, my feeling is that it is illogical.\r<BR>\n" );
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document.write( "Indeed, it asks, how many partitions of 17 are there that have at least three parts.\r<BR>\n" );
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document.write( "\"At least  three parts\" includes/allows 3 parts, but then it impose some conditions <BR>\n" );
document.write( "on the fourth part (which may absent).\r<BR>\n" );
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document.write( "In Math, it is prohibited to write such a gibberish and then to sell (to position) it as a \"problem\".\r<BR>\n" );
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document.write( "To the author: you may write gibberish, \r<BR>\n" );
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document.write( "- - - - - - - - - - - - - - - but do not forget then to throw it into the garbage bin.\r<BR>\n" );
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document.write( "Or hire a special person (like me), who will do it for you.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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