AMC8 2020

AMC8 2020 · Q6

AMC8 2020 · Q6. It mainly tests Logic puzzles.

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?

Aaron、Darren、Karen、Maren 和 Sharon 乘坐一列小型火车，这列火车有五个座位，每个座位容纳一人。Maren 坐在最后一节车厢。Aaron 坐在 Sharon 正后面。Darren 坐在 Aaron 前面的某个车厢。Karen 和 Darren 之间至少坐着一个人。谁坐在中间车厢？

(A) \text{Aaron} \text{Aaron}

(B) \text{Darren} \text{Darren}

(D) \text{Maren} \text{Maren}

(E) \text{Sharon} \text{Sharon}

Answer

Correct choice: (A)

正确答案：（A）

Solution

Write the order of the cars as $\square\square\square\square\square$, where the left end of the row represents the back of the train and the right end represents the front. Call the people $A$, $D$, $K$, $M$, and $S$ respectively. The first condition gives $M\square\square\square\square$, so we try $MAS\square\square$, $M\square AS\square$, and $M\square\square AS$. In the first case, as $D$ sat in front of $A$, we must have $MASDK$ or $MASKD$, which do not comply with the last condition. In the second case, we obtain $MKASD$, which works, while the third case is obviously impossible since it results in there being no way for $D$ to sit in front of $A$. It follows that, with the only possible arrangement being $MKASD$, the person sitting in the middle car is $\boxed{\textbf{(A) }\text{Aaron}}$.

将车厢顺序写成 $\square\square\square\square\square$，其中行左端代表火车尾部，右端代表火车头部。分别称呼这些人 $A$、$D$、$K$、$M$ 和 $S$。第一个条件给出 $M\square\square\square\square$，所以我们尝试 $MAS\square\square$、$M\square AS\square$ 和 $M\square\square AS$。在第一种情况下，由于 $D$ 坐在 $A$ 前方，我们必须有 $MASDK$ 或 $MASKD$，这些都不符合最后一个条件。在第二种情况下，我们得到 $MKASD$，这可行，而第三种情况显然不可能，因为无法让 $D$ 坐在 $A$ 前方。因此，只有可能的排列是 $MKASD$，中间车厢的人是 $\boxed{\textbf{(A) }\text{Aaron}}$。

Topics

LM.001 Logic puzzles