document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=967817>Question 967817</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I want to put a tennis schedule together. There will be 12 players or six double teams. I need a schedule that in 11 matches no one plays anyone twice. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #591556 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=591556\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you have 6 double teams.<BR>\n" );
document.write( "out of those 6 double teams, you can make c(6,2) combinations where each pair is different.\r<BR>\n" );
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document.write( "c(6,2) is equal to 6! / (2! * 4!) which is equal to (6*5)/2 = 15 different combinations where order is not important.\r<BR>\n" );
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document.write( "order is not important means that ab and ba count as one game, not two.<BR>\n" );
document.write( "if order was important, they would count as two games.\r<BR>\n" );
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document.write( "let the teams be labeled team a, b, c, d, e, f.\r<BR>\n" );
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document.write( "the 15 possible different combinations where order is not important are:\r<BR>\n" );
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document.write( "ab<BR>\n" );
document.write( "ac<BR>\n" );
document.write( "ad<BR>\n" );
document.write( "ae<BR>\n" );
document.write( "af\r<BR>\n" );
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document.write( "bc<BR>\n" );
document.write( "bd<BR>\n" );
document.write( "be<BR>\n" );
document.write( "bf\r<BR>\n" );
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document.write( "cd<BR>\n" );
document.write( "ce<BR>\n" );
document.write( "cf\r<BR>\n" );
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document.write( "de<BR>\n" );
document.write( "df\r<BR>\n" );
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document.write( "ef\r<BR>\n" );
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document.write( "if you want every team to play every other team where no teams plays the same team twice, then you can schedule 15 matches and that will do it.\r<BR>\n" );
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document.write( "otherwise, if you can only schedule 11 matches, then pick any 11 out of the 15.\r<BR>\n" );
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document.write( "you might want to count how many games each team is in so you can even it up as much as possible.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "ab counts as one for a and one for b.<BR>\n" );
document.write( "bc counts as one for b and one for c.<BR>\n" );
document.write( "total for a is 1<BR>\n" );
document.write( "total for b is 2<BR>\n" );
document.write( "total for c is 1.<BR>\n" );
document.write( "cd counts as one for c and one for d.<BR>\n" );
document.write( "total for c is now 2.<BR>\n" );
document.write( "total for d is 1.<BR>\n" );
document.write( "etc.\r<BR>\n" );
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document.write( "the goal is to even up the number of games as much as possible.<BR>\n" );
document.write( "you won't be able to make each team play exactly the same number of games, but you can make them more or less even.\r<BR>\n" );
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document.write( "one possible arrangement would be:\r<BR>\n" );
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document.write( "ab<BR>\n" );
document.write( "ac<BR>\n" );
document.write( "af<BR>\n" );
document.write( "bc<BR>\n" );
document.write( "bd<BR>\n" );
document.write( "be<BR>\n" );
document.write( "cd<BR>\n" );
document.write( "ce<BR>\n" );
document.write( "de<BR>\n" );
document.write( "df<BR>\n" );
document.write( "ef\r<BR>\n" );
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document.write( "you have a count of:<BR>\n" );
document.write( "a = 3<BR>\n" );
document.write( "b = 4<BR>\n" );
document.write( "c = 4<BR>\n" );
document.write( "d = 4<BR>\n" );
document.write( "e = 4<BR>\n" );
document.write( "f = 3\r<BR>\n" );
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document.write( "add them up and they total 22.<BR>\n" );
document.write( "divide that by 2 and you get 11 games.\r<BR>\n" );
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document.write( "that's about as even as you'll be able to get it with 11 games.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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