2014 AMC 8 Problems/Problem 16: Difference between revisions
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Revision as of 13:19, 5 November 2017
Problem
The "Middle School Eight" basketball conference has 
teams. Every season, each team plays every other conference team twice (home and away), and each team also plays 
games against non-conference opponents. What is the total number of games in a season involving the "Middle School Eight" teams?
Solution
Within the conference, there are 8 teams, so there are 
pairings of teams, and each pair must play two games, for a total of 
games within the conference.
Each team also plays 4 games outside the conference, and there are 8 teams, so there are a total of 
games outside the conference.
Therefore, the total number of games is 
, so 
is our answer.
See Also
Template:AMC8 boylear=2014 These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. Error creating thumbnail: File missing
