Question

五位朋友坐在电影院同一排的 $5$ 个座位上，座位从左到右编号为 $1$ 到 $5$ 。（“左”和“右”从坐在座位上的人的视角看。）电影中途 Ada 去大厅买爆米花。她回来时发现 Bea 向右移动了两个座位，Ceci 向左移动了一个座位， Dee 和 Edie 交换了座位，并给 Ada 留下了一个端座。Ada 起身前坐在哪个座位？

Five friends sat in a movie theater in a row containing $5$ seats, numbered $1$ to $5$ from left to right. (The directions "left" and "right" are from the point of view of the people as they sit in the seats.) During the movie Ada went to the lobby to get some popcorn. When she returned, she found that Bea had moved two seats to the right, Ceci had moved one seat to the left, and Dee and Edie had switched seats, leaving an end seat for Ada. In which seat had Ada been sitting before she got up?

$1$

$2$

$3$

$4$

$5$

答案：B

知识点：不变量逻辑推理

难度评级：1410

解答：

五位朋友的总位移为零。Dee 和 Edie 交换座位，所以两人的位移相互抵消。Bea 移动 $+2$ 个座位，Ceci 移动 $-1$ 个座位，净位移为 $+1$ ，所以 Ada 必须移动 $-1$ 个座位才能抵消。

Ada 回来后坐在端座；既然她向左移动了一个座位，该端座只能是 $1$ 号座，所以她原来坐在 $2$ 号座。

所以正确答案是 B。

The net displacement of all five friends is zero. Dee and Edie swapped seats, so their movements cancel. Bea moved $+2$ and Ceci moved $-1,$ a net of $+1,$ so Ada must move $-1$ to balance.

Ada returns to an end seat; since she moved one seat to the left, that seat must be seat $1,$ so she had been sitting in seat $2.$

Thus, the correct answer is B.

2016 AMC 12A 第 10 题

答案：B

难度评级：1410

解答：

其他年份的第 10 题