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?  Choose the most appropriate option
A) 79  B) 83  C) 85  D) 87  E) 88
Consider 4 teams.   Max possible games if a team is eliminated after 2 loses = 3 + 2= 
<gadget id="calculator">3 + 2</gadget>
<output>5</output>
5   Similarly, if 5 teams are there,   Max possible games= 4 + 3= 
<gadget id="calculator">4 + 3</gadget>
<output>7</output>
7.   So going forth we can play 15,17,19,21 max possible games for 9,10,11,12 teams respectively.   Adding them up gives 72. Now there are two teams left in each group still. So four more games to give a winner in each team.   So 72+ 4= 
<gadget id="calculator">72+ 4</gadget>
<output>76</output>
76.   Now of the four teams we can have max 3 games if its a knock out round.   So 76 + 3= 
<gadget id="calculator">76 + 3</gadget>
<output>79</output>
79.   79nswer 79= 79.
<result>A</result>
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?