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## Discussion topic: Puzzles & Brain Teasers : Football Matches

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 Page 1 of 1 From: syvum Reply 1 of 2 Reply 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: buttafucco Reply 2 of 2 Reply 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) Page 1 of 1