Question

四名学生坐成一排。他们可以和坐在自己旁边的人聊天。现在重新安排座位，使得没有任何一对原来相邻的学生仍然相邻。这样的重新安排有多少种？

Four students are seated in a row. They chat with the people sitting next to them, then rearrange themselves so that they are no longer seated next to any of the same people. How many rearrangements are possible?

$2$

$4$

$9$

$12$

$24$

答案：A

知识点：有限制的排列排列

难度评级：1450

视频讲解：

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文字解答：

设原顺序为 $A,B,C,D$ 。禁止相邻的配对是 $AB$ 、 $BC$ 、 $CD$ ，所以只允许 $AC$ 、 $AD$ 、 $BD$ 相邻。四人排成一排会有三对相邻位置，因此这三对必须全部出现，只能是 $C,A,D,B$ 或其反向。共有 $2$ 种。

Name the original order $A,B,C,D$ . The forbidden neighboring pairs are $AB$ , $BC$ , and $CD$ , so the only allowed pairs are $AC$ , $AD$ , and $BD$ . To seat all four students in a row, the three row-adjacencies must be exactly these three edges, giving $C,A,D,B$ or its reverse. There are $2$ rearrangements.

2026 AMC 8 第 17 题

答案：A

难度评级：1450

视频讲解：

文字解答：

其他年份的第 17 题