Question

Little Twelve Basketball Conference 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。共安排了多少场联盟比赛？

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?

$80$

$96$

$100$

$108$

$192$

答案：B

知识点：双重计数基本计数

难度评级：1220

解答：

关注一支球队。它与本分区另外 $5$ 支球队各比赛两次，共 $2 \cdot 5 = 10$ 场。

它还与另一分区的 $6$ 支球队各比赛一场，所以总共打 $10 + 6 = 16$ 场。

共有 $12$ 支球队，于是按球队计数为 $12 \cdot 16 = 192$ 场。但每场比赛涉及 $2$ 支球队，所以要除以 $2$ 。

实际总场数为 $192 \div 2 = 96$ 。

所以正确答案是 B。

Let us focus on one team. This team plays against $5$ other teams twice in its own division, for a total of $2 \cdot 5 = 10$ games.

This team also plays $6$ games with teams from the other division. Therefore, they play a total of $10 + 6 = 16$ games.

There are $12$ teams total, so there are $12 \cdot 16 = 192$ games conducted. Each game, however, involves $2$ teams, so we have to divide by $2.$

This gives us the actual total number of games to be $192 \div 2 = 96.$

Thus, B is the correct answer.

2005 AMC 8 第 14 题

答案：B

难度评级：1220

解答：

其他年份的第 14 题