2003 AMC 8 第 17 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。
17.
下面列出的六个孩子来自两个家庭，每个家庭有三个兄弟姐妹。每个孩子有蓝色或棕色眼睛，以及黑色或金色头发。同一个家庭的孩子至少有其中一个特征相同。哪两个孩子是 Jim 的兄弟姐妹？
| 姓名 | 眼睛颜色 | 头发颜色 |
|---|---|---|
| Benjamin | 蓝色 | 黑色 |
| Jim | 棕色 | 金色 |
| Nadeen | 棕色 | 黑色 |
| Austin | 蓝色 | 金色 |
| Tevyn | 蓝色 | 黑色 |
| Sue | 蓝色 | 金色 |
The six children listed below are from two families of three siblings each. Each child has blue or brown eyes and black or blond hair. Children from the same family have at least one of these characteristics in common. Which two children are Jim’s siblings?
| Child | Eye Color | Hair Color |
|---|---|---|
| Benjamin | Blue | Black |
| Jim | Brown | Blond |
| Nadeen | Brown | Black |
| Austin | Blue | Blond |
| Tevyn | Blue | Black |
| Sue | Blue | Blond |
Nadeen 和 Austin
Nadeen and Austin
Benjamin 和 Sue
Benjamin and Sue
Benjamin 和 Austin
Benjamin and Austin
Nadeen 和 Tevyn
Nadeen and Tevyn
Austin 和 Sue
Austin and Sue
答案：E
小提示：
Jim 的兄弟姐妹必须各自与 Jim 共享眼睛颜色或头发颜色
Jim’s siblings must each share eye color or hair color with Jim.
大提示：
这两个兄弟姐妹彼此之间也必须至少共享一个特征
The two siblings must also share at least one characteristic with each other.
解答：
Nadeen、Austin 和 Sue 是唯一与 Jim 共享某个特征的 个人。需要找出其中哪一个与其他人完全不同。
Austin 和 Sue 都有蓝色眼睛，所以 Nadeen 是不属于这一组的人。因此 Austin 和 Sue 是 Jim 的兄弟姐妹。
所以正确答案是 E。
Note that Nadeen, Austin, and Sue are the only individuals who share a characteristic with Jim. We need to find which of the are completely different from the others.
Austin and Sue both have blue eyes, which makes Nadeen the odd one out. Therefore, Austin and Sue are Jim’s siblings.
Thus, E is the correct answer.
其他年份的第 17 题
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