AMC12 2016 A

AMC12 2016 A · Q10

AMC12 2016 A · Q10. It mainly tests Logic puzzles, Invariants.

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?

五个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”的方向以坐在座位上的人自身视角为准。）电影过程中，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互换了座位，从而给Ada留下了一个靠边的座位。Ada起身前原来坐在哪个座位上？

(A) 1 1

(B) 2 2

(D) 4 4

(E) 5 5

Answer

Correct choice: (B)

正确答案：（B）

Solution

Answer (B): The total number of seats moved to the right among the five friends must equal the total number of seats moved to the left. One of Dee and Edie moved some number of seats to the right, and the other moved the same number of seats to the left. Because Bea moved two seats to the right and Ceci moved one seat to the left, Ada must also move one seat to the left upon her return. Because her new seat is an end seat and its number cannot be 5, it must be seat 1. Therefore Ada occupied seat 2 before she got up. The order before moving was Bea-Ada-Ceci-Dee-Edie (or Bea-Ada-Ceci-Edie-Dee), and the order after moving was Ada-Ceci-Bea-Edie-Dee (or Ada-Ceci-Bea-Dee-Edie).

答案（B）：五位朋友向右移动的座位总数必须等于向左移动的座位总数。Dee 和 Edie 中有一人向右移动若干个座位，另一人向左移动相同的座位数。由于 Bea 向右移动了两个座位，而 Ceci 向左移动了一个座位，Ada 回来时也必须向左移动一个座位。因为她的新座位在最末端且其编号不能为 5，所以必定是 1 号座位。因此 Ada 起身前坐在 2 号座位上。移动前的顺序是 Bea-Ada-Ceci-Dee-Edie（或 Bea-Ada-Ceci-Edie-Dee），移动后的顺序是 Ada-Ceci-Bea-Edie-Dee（或 Ada-Ceci-Bea-Dee-Edie）。

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