2020 AMC 8 第 6 题
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所有题目均经美国数学协会（MAA）官方合法授权使用。
6.
亚伦、达伦、凯伦、玛伦和莎伦乘坐一列小火车，火车有五节车厢，每节坐一人。玛伦坐在最后一节车厢。亚伦正好坐在莎伦后面。达伦坐在亚伦前面的某节车厢。凯伦和达伦之间至少隔着一个人。谁坐在中间车厢？
Aaron, Darren, Karen, Maren, and Sharon rode on a small train that has five cars that seat one person each. Maren sat in the last car. Aaron sat directly behind Sharon. Darren sat in one of the cars in front of Aaron. At least one person sat between Karen and Darren. Who sat in the middle car?
亚伦
Aaron
达伦
Darren
凯伦
Karen
玛伦
Maren
莎伦
Sharon
小提示：
玛伦固定在最后一节车厢
Maren is fixed in the last car
大提示：
检查莎伦和亚伦相邻的可能位置
Test the possible adjacent positions for Sharon and Aaron
视频讲解：
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文字解答：
玛伦坐在最后一节。由于亚伦正好在莎伦后面，且达伦在亚伦前方，在玛伦前面的车厢中只需安排达伦、莎伦和亚伦的相对位置。
如果莎伦和亚伦分别在第 和第 节，达伦就无法坐在亚伦前面；如果他们在第 和第 节，达伦和凯伦只能在第 和第 节，会相邻。
因此莎伦和亚伦必须在第 和第 节，达伦在第 节，凯伦在第 节，亚伦坐在中间车厢。
正确答案是 A。
Maren is in the last car. Since Aaron is directly behind Sharon and Darren is in front of Aaron, the possible placements of Darren, Sharon, and Aaron before Maren are limited.
If Sharon and Aaron were in cars and Darren could not be in front of Aaron. If they were in cars and then Darren and Karen would have to occupy cars and which are adjacent.
Thus Sharon and Aaron must be in cars and Darren is then in car Karen is in car and Aaron is in the middle car.
Thus, the correct answer is A.
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