document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1059824>Question 1059824</A>: <I><SPAN STYLE=\"word-break: break-all;\"> After winning the championship, all Dallas Maverick teammates hugs. Altogether there were 66 hugs. How many players were there? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #674906 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=674906\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x = number of players\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "A player cannot hug themself, so there are x-1 choices for any one player to hug. <BR>\n" );
document.write( "There are x*(x-1) ways to have players hug assuming order mattered (eg: AB is different from BA)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "However, player A hugging player B is the same as B hugging A. Order does not matter. This means we must correct for the double count by dividing by 2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The expression for the number of hugs is x*(x-1)/2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Set this equal to 66 and solve for x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x*(x-1)/2 = 66\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2*x*(x-1)/2 = 66*2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x*(x-1) = 132\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x^2 - x = 132\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x^2 - x - 132 = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(x - 12)(x + 11) = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x - 12 = 0 or x + 11 = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x = 12 or x = -11\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Toss out the negative number. Only x = 12 makes sense\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So there are 12 players on the team.  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );