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Pretty Tough Question - Need some help

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Pretty Tough Question - Need some help

by Tame the CAT » Mon May 07, 2007 11:52 am
A certain league has four divisions. The respective divisions had 9, 10, 11, and 12 teams qualify for the playoffs. Each division held its own double-elimination tournament -- where a team is eliminated from the tournament upon losing two games -- in order to determine its champion. The four division champions then played in a single-elimination tournament -- where a team is eliminated upon losing one game -- in order to determine the overall league champion. Assuming that there were no ties and no forfeits, what is the maximum number of games that could have been played in order to determine the overall league champion?

(A) 79
(B) 83
(C) 85
(D) 87
(E) 88

BTW, I didn't see the answer/solution yet. I will definitely post it later
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by sanju09 » Wed Jul 28, 2010 4:34 am
Tame the CAT wrote:A certain league has four divisions. The respective divisions had 9, 10, 11, and 12 teams qualify for the playoffs. Each division held its own double-elimination tournament -- where a team is eliminated from the tournament upon losing two games -- in order to determine its champion. The four division champions then played in a single-elimination tournament -- where a team is eliminated upon losing one game -- in order to determine the overall league champion. Assuming that there were no ties and no forfeits, what is the maximum number of games that could have been played in order to determine the overall league champion?

(A) 79
(B) 83
(C) 85
(D) 87
(E) 88

BTW, I didn't see the answer/solution yet. I will definitely post it later
Please wait Tame the CAT...

The scenario is equivalent to a total of 42 teams playing on knock-out basis to get to a single champion team; 42 is an even number of teams and hence it would require [spoiler]2 × 42 + 1 = 85[/spoiler] games that should be played in order to determine the overall league champion.

[spoiler]C[/spoiler]
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