2006 AMC 8 第 22 题
先试着解答 2006 AMC 8 第 22 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 2006 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。
22.
三个不同的一位正整数放在底行格子中。相邻格子的数相加，和放在它们上方的格子中。在第二行继续同样过程，得到顶格中的数。顶格中可能的最大数与最小数之差是多少？
Three different one-digit positive integers are placed in the bottom row of cells. Numbers in adjacent cells are added and the sum is placed in the cell above them. In the second row, continue the same process to obtain a number in the top cell. What is the difference between the largest and smallest numbers possible in the top cell?
答案：D
小提示：
将底行三个数写成 、 和 。
Write the three bottom entries as and .
大提示：
底行中间的数在顶格中被计算两次。
The middle bottom entry is counted twice in the top number.
解答：
如果底行格子中的数依次为 、 和 ，那么中间一行就是 和 。
因此顶格为 。要使它最小，把 放在中间，外侧放 和 ，得到顶格数 。
要使它最大，把 放在中间，外侧放 和 ，得到顶格数 。所求差为 。
所以正确答案是 D。
If the lower cells contain and the middle row will have and .
This means that the top row will have . To minimize this, put in the middle and and in the outer cells. This yields a top number of .
To maximize it, put in the middle and and in the outer cells. This yields a top number of . The desired difference is .
Thus, D is the correct answer.
其他年份的第 22 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
- 2003 AMC 8
- 2004 AMC 8
- 2005 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