2005 AMC 8 Problem 14
Attempt Problem 14 of the 2005 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 2005 AMC 8 solutions, or check the answer key.
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14.
The Little Twelve Basketball Conference has two divisions, with six teams in each division. Each team plays each of the other teams in its own division twice and every team in the other division once. How many conference games are scheduled?
Answer: B
Small hint:
Count each team’s games, then correct for double-counting.
Big hint:
Each game is counted once for each of its two teams.
Solution:
Let us focus on one team. This team plays against other teams twice in its own division, for a total of games.
This team also plays games with teams from the other division. Therefore, they play a total of games.
There are teams total, so there are games conducted. Each game, however, involves teams, so we have to divide by
This gives us the actual total number of games to be
Thus, B is the correct answer.
Problem 14 in other years
- 1985 AMC 8
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