1991 AMC 8 第 24 题
先试着解答 1991 AMC 8 第 24 题，然后核对你的答案与精心整理的解答，解答来自 LIVE by Po-Shen Loh。你也可以参加完整限时模拟考试、查看全部 1991 AMC 8 解答，或核对答案。
所有题目均经美国数学协会（MAA）官方合法授权使用。
24.
一个边长为 厘米的正方体被切成 个较小的正方体，且这些小正方体不全同样大小。如果每个小正方体的边长都是整厘米数，那么
A cube of edge cm is cut into smaller cubes, not all the same size. If the edge of each of the smaller cubes is a whole number of centimeters, then
小提示：
小正方体的边长必须是整数，所以只能是边长 或边长
The smaller cubes must have whole-number edges, so each is edge or edge
大提示：
只能放下一个边长为 的正方体；剩下的体积 用单位正方体填满
Only one edge- cube fits; the rest are unit cubes filling the remaining volume
解答：
这个 正方体的体积是 。由于小正方体更小且边长为整数，它们的边长只能是 或 。原正方体内不能放下两个互不相交的边长为 的正方体，因为要将它们分开，某个方向上的总跨度至少为 。因此最多只能放下一个边长为 的正方体。
剩余体积 ，由 个单位正方体填满。总数是 个正方体。
所以正确答案是 E。
The cube has volume Since the cubes are smaller and have whole-number edge lengths, their edges are or . Two edge- cubes cannot be disjoint inside the original cube: separating them would require a total span of at least in some direction. Thus at most one edge- cube fits.
The remaining of volume is filled by unit cubes. That is cubes.
Thus, the correct answer is E .
其他年份的第 24 题
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 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
- 2003 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