1996 AMC 8 第 14 题
先试着解答 1996 AMC 8 第 14 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 1996 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。
14.
从集合 中选出六个不同数字，填入下图的方格中，使竖直列中各数之和为 ，水平行中各数之和为 。所用六个数字之和是
Six different digits from the set are placed in the squares in the figure shown so that the sum of the entries in the vertical column is and the sum of the entries in the horizontal row is The sum of the six digits used is
小提示：
三个不同数字和为 ，只能是 、、。
Three distinct digits summing to must be and
大提示：
共享方格在两次求和中都被计算了，所以六个数字总和等于 减去共享数字。
The shared square is counted in both sums, so the total of the six digits is minus the shared digit
解答：
从 到 中选三个不同数字和为 ，只能是 、、。水平行另外三个数字最小为 ，所以共享方格至多是 。因此共享数字是 。
六个数字是 、、、、、，总和为 。等价地，。
所以正确答案是 B。
Three distinct digits from through summing to must be and The row’s other three digits are at least so the shared square (belonging to both the column and the row) is at most Hence the shared digit is
The six digits are then and whose sum is Equivalently,
Thus, the correct answer is B .
其他年份的第 14 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
- 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