2005 AMC 8 第 14 题
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所有题目均经美国数学协会（MAA）官方合法授权使用。
14.
小十二篮球联盟有两个分区，每个分区有六支球队。每支球队与本分区其他每支球队比赛两次，并与另一分区每支球队比赛一次。联盟共安排了多少场比赛？
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?
小提示：
先数每支球队的比赛数，再修正重复计数
Count each team’s games, then correct for double-counting.
大提示：
每场比赛会被两支球队各数一次
Each game is counted once for each of its two teams.
解答：
关注一支球队。它与本分区另外 支球队各比赛两次，共 场。
它还与另一分区的 支球队各比赛一场，所以总共打 场。
共有 支球队，于是按球队计数为 场。但每场比赛涉及 支球队，所以要除以 。
实际总场数为 。
所以正确答案是 B。
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.
其他年份的第 14 题
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