1973 AMC 12 第 2 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。
2.
将一千个单位立方体粘成一个棱长为 个单位的大立方体；把大立方体涂色后，再拆成原来的小立方体。至少有一个面被涂色的单位立方体个数为
One thousand unit cubes are fastened together to form a large cube with edge length units; this is painted and then separated into the original cubes. The number of these unit cubes which have at least one face painted is
小提示：
改为计算没有任何一面被涂色的小立方体个数
Count the cubes with no painted face instead
大提示：
去掉外层后，剩下一个 的立方体
Removing the outer layer leaves an cube
解答：
没有被涂色的小立方体恰好组成内部的 立方体。因此至少有一个面被涂色的小立方体个数为
所以正确答案是 C。
The unpainted cubes are precisely the interior cube. Therefore the number having at least one painted face is
Therefore, the correct answer is C.
其他年份的第 2 题
- 1950 AMC 12
- 1951 AMC 12
- 1952 AMC 12
- 1953 AMC 12
- 1954 AMC 12
- 1955 AMC 12
- 1956 AMC 12
- 1957 AMC 12
- 1958 AMC 12
- 1959 AMC 12
- 1960 AMC 12
- 1961 AMC 12
- 1962 AMC 12
- 1963 AMC 12
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- 1965 AMC 12
- 1966 AMC 12
- 1967 AMC 12
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- 2002 AMC 12A
- 2002 AMC 12B
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- 2003 AMC 12B
- 2004 AMC 12A
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- 2005 AMC 12A
- 2005 AMC 12B
- 2006 AMC 12A
- 2006 AMC 12B
- 2007 AMC 12A
- 2007 AMC 12B
- 2008 AMC 12A
- 2008 AMC 12B
- 2009 AMC 12A
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- 2010 AMC 12A
- 2010 AMC 12B
- 2011 AMC 12A
- 2011 AMC 12B
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- 2012 AMC 12B
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- 2014 AMC 12A
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- 2020 AMC 12B
- 2021 AMC 12A Spring
- 2021 AMC 12B Spring
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- 2021 AMC 12B Fall
- 2022 AMC 12A
- 2022 AMC 12B
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- 2023 AMC 12B
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- 2025 AMC 12A
- 2025 AMC 12B