document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=845402>Question 845402</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am looking for a mathematical formula (equation) for the following scenario:\r<BR>\n" );
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document.write( "A challenge is played by X number of participants.<BR>\n" );
document.write( "Each participant contributes the same number of Y points to the challenge (when they join).<BR>\n" );
document.write( "Thus, the total points in the challenge at any given time is: X*Y points.\r<BR>\n" );
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document.write( "The points ares distributed according to the following rule (for which I need a formula):<BR>\n" );
document.write( "1. The person in 1st place, takes 50% of the points.<BR>\n" );
document.write( "2. For the remaining (X-1) participants, the remaining points are distributed in a descending order of value.\r<BR>\n" );
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document.write( "e.g. Challenge A has 10 participants and each participant puts in 10,000 points. With total points in the challenge being 100,000 points.\r<BR>\n" );
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document.write( "Person in the 1st place gets - 50,000 points<BR>\n" );
document.write( "The remaining 9 participants get the remaining 50,000 points distributed in a decreasing order of value<BR>\n" );
document.write( "For example (one such scenario):<BR>\n" );
document.write( "#2 - 12,000<BR>\n" );
document.write( "#3 - 10,000<BR>\n" );
document.write( "#4 - 9,000<BR>\n" );
document.write( "#5 - 8,000<BR>\n" );
document.write( "#6 - 5,000<BR>\n" );
document.write( "#7 - 3,000<BR>\n" );
document.write( "#8 - 2,000<BR>\n" );
document.write( "#9 - 1,000\r<BR>\n" );
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document.write( "Can this be modeled mathematically?\r<BR>\n" );
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document.write( "Thank you.<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 #514571 by </B><A HREF=/tutors/aboutme.mpl?userid=richwmiller><B>richwmiller(17219)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richwmiller><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=richwmiller><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=514571\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> z=x*y<BR>\n" );
document.write( "p=z/2<BR>\n" );
document.write( "p = ½(2a + d(n-1))n<BR>\n" );
document.write( "n=x-1<BR>\n" );
document.write( "d=-1<BR>\n" );
document.write( "a= second prize\r<BR>\n" );
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document.write( "in your example,<BR>\n" );
document.write( "x=10<BR>\n" );
document.write( "y=10000<BR>\n" );
document.write( "z=100000<BR>\n" );
document.write( "p=50000,<BR>\n" );
document.write( "n=9,<BR>\n" );
document.write( "d=-1,<BR>\n" );
document.write( "a=5559.56<BR>\n" );
document.write( "p = ½(2a + d(n-1))n\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );