2014 AMC 8 Problem 16
Attempt Problem 16 of the 2014 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2014 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
16.
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?
Answer: B
Small hint:
Count non-conference games separately from conference games.
Big hint:
For conference games, count each team’s home games against the other seven teams.
Solution:
Each team plays non-conference games, for games involving Middle School Eight teams and non-conference opponents.
Within the conference, each of the teams has home games against the other teams, so there are conference games. The total is .
Thus, B is the correct answer.
Problem 16 in other years
- 1985 AMC 8
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