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)
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| 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)
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