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From: syvumReply 1 of 2Reply
Subject: Puzzles & Brain Teasers : Football Matches
   Discuss this puzzle with other Syvum members in this forum.	If you have
   alternative solution procedures, or questions about this puzzles, feel free
   to post them here.

Posted at: Sun Jul 13 03:39:21 2003 (GMT)

From: buttafuccoReply 2 of 2Reply
Subject: alternative solution
   Problem seems to be a combination.  Using the nCr(n!/(r!(n-r)!) notation,
   and knowing that we are choosing 2 teams at a time, the formula for 78 games
   would reduce to:
   
	      78 =  n!/(2!(n-2)!)
   
   if imagining a fraction bar would look like:
    
	      78 =     n!
		    2!(n-2)!
   
   which equals 78*2! = n!/(n-2)!
   
   which equals 156 = n!/(n-2)!
   
   which equals 156 = n(n-1)  =====> imagine 5!/(5-2)! = 120/6
				     which is 5*4
   
   then you have n^2 - n - 156 = 0
   
   which can be factored to (n-13)(n+12) = 0
   
   so n = 13
   (n = -12 is ignored because you cannot have negative teams)

Posted at: Fri Feb 11 18:19:28 2005 (GMT)

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