2012 AMC 8 Problem 14
Attempt Problem 14 of the 2012 AMC 8 below, then check your answer against the video solution and professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2012 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
14.
In the BIG N, a middle school football conference, each team plays every other team exactly once. If a total of conference games were played during the season, how many teams were members of the BIG N conference?
Answer: B
Small hint:
List how many games are added when each new team joins.
Big hint:
With teams, the number of games is .
Video solution:
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Written solution:
Each of the teams plays games. However, teams play each game, so multiplying and would be twice the number of games. Therefore, we know This leads to which implies In turn, this suggests:
Thus, the answer is B .
Problem 14 in other years
- 1985 AMC 8
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