2003 AMC 8 第 13 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。
13.
十四个白色立方体拼成右图。这个立体的整个表面，包括底面，都被涂成红色。然后将这个立体拆成单个立方体。有多少个单个立方体恰好有四个面是红色的？
Fourteen white cubes are put together to form the figure on the right. The complete surface of the figure, including the bottom, is painted red. The figure is then separated into individual cubes. How many of the individual cubes have exactly four red faces?
小提示：
一个小立方体恰好有四个涂色面，当且仅当它接触两个其他立方体
A cube has four painted faces exactly when it touches two other cubes.
大提示：
分别考虑顶部立方体、底部角落立方体和剩余立方体
Separate the top cubes, bottom corner cubes, and remaining cubes.
解答：
一个小立方体恰好有四个面被涂色，当且仅当它恰好与两个其他立方体相连。
个顶部立方体只接触一个其他立方体，所以它们有 个涂色面。 个底部角落立方体接触三个其他立方体，所以它们有 个涂色面。
剩下的 个立方体各恰好接触两个其他立方体，所以它们恰好有四个涂色面。
所以正确答案是 B。
A cube has exactly four painted faces exactly when it is attached to exactly two other cubes.
The top cubes touch only one other cube, so they have painted faces. The bottom corner cubes touch three other cubes, so they have painted faces.
The remaining cubes each touch exactly two other cubes, so they have exactly four painted faces.
Thus, B is the correct answer.
其他年份的第 13 题
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
- 1992 AMC 8
- 1993 AMC 8
- 1994 AMC 8
- 1995 AMC 8
- 1996 AMC 8
- 1997 AMC 8
- 1998 AMC 8
- 1999 AMC 8
- 2000 AMC 8
- 2001 AMC 8
- 2002 AMC 8
- 2004 AMC 8
- 2005 AMC 8
- 2006 AMC 8
- 2007 AMC 8
- 2008 AMC 8
- 2009 AMC 8
- 2010 AMC 8
- 2011 AMC 8
- 2012 AMC 8
- 2013 AMC 8
- 2014 AMC 8
- 2015 AMC 8
- 2016 AMC 8
- 2017 AMC 8
- 2018 AMC 8
- 2019 AMC 8
- 2020 AMC 8
- 2022 AMC 8
- 2023 AMC 8
- 2024 AMC 8
- 2025 AMC 8
- 2026 AMC 8