Question

Samantha 住在 City Park 西南角以西 $2$ 个街区、以南 $1$ 个街区的地方。

她的学校在 City Park 东北角以东 $2$ 个街区、以北 $2$ 个街区的地方。上学日她先沿街骑车到 City Park 的西南角，再走公园里的对角线小路到东北角，然后沿街骑车到学校。

如果她的路线尽可能短，她有多少种不同路线可走？

Samantha lives $2$ blocks west and $1$ block south of the southwest corner of City Park.

Her school is $2$ blocks east and $2$ blocks north of the northeast corner of City Park. On school days she bikes on streets to the southwest corner of City Park, then takes a diagonal path through the park to the northeast corner, and then bikes on streets to school.

If her route is as short as possible, how many different routes can she take?

$3$

$6$

$9$

$12$

$18$

答案：E

知识点：格路乘法原理

难度评级：1540

视频讲解：

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文字解答：

为了最快到达公园西南角，Samantha 必须向东走 $2$ 个街区、向北走 $1$ 个街区，这些步骤可排列成 $3$ 种方式。经过公园对角线小路后，她必须再向东走 $2$ 个街区、向北走 $2$ 个街区到学校，这些步骤可排列成 $\binom{4}{2}=6$ 种方式。

公园前后的选择相互独立，所以最短路线总数为 $3\cdot6=18$ 。

所以正确答案是 E。

To reach the southwest corner of the park as quickly as possible, Samantha must go $2$ blocks east and $1$ block north, which can be arranged in $3$ ways. After the diagonal path through the park, she must go $2$ blocks east and $2$ blocks north to reach school, which can be arranged in $\binom{4}{2}=6$ ways.

The choices before and after the park are independent, so the total number of shortest routes is $3\cdot6=18$ .

Thus, E is the correct answer.

2013 AMC 8 第 21 题

答案：E

难度评级：1540

视频讲解：

文字解答：

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