Question

五位朋友坐在电影院一排 $5$ 个座位中，从左到右编号为 $1$ 到 $5$ 。（“左”和“右”是从坐在座位上的人的视角看。）

电影期间 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，并且给 Ada 留下了一个端点座位。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：逻辑推理不变量

难度评级：1420

解答：

移动前后，被占用座位编号之和都是 $1+2+3+4+5=15$ 。Dee 和 Edie 只是交换座位，所以两人的合位移为 $0.$ Bea 的位移为 $+2,$ Ceci 的位移为 $-1.$ 因此为了使总位移为 $0.$ Ada 的位移必须为 $-1$ 。

Ada 最后回到一个端点座位。因为她向左移动一个座位，所以她必定从 $2$ 号座位移到 $1.$ 号座位。

所以正确答案是 B。

The sum of the occupied seat numbers is $1+2+3+4+5=15$ both before and after the moves. Dee and Edie merely switch seats, so their combined displacement is $0.$ Bea's displacement is $+2,$ and Ceci's is $-1.$ Therefore Ada's displacement must be $-1$ so that the total displacement is $0.$

Ada returns to an end seat. Since she moves one seat left, she must move from seat $2$ to seat $1.$

Thus, the correct answer is B .

2016 AMC 10A 第 13 题

答案：B

难度评级：1420

解答：

其他年份的第 13 题