AMC 8 1999 Problem 11
AMC8 1999 年第 11 题
基本计数原理★★★☆☆
Each of the five numbers 1, 4, 7, 10, and 13 is placed in one of the five squares so that the sum of the three numbers in the horizontal row equals the sum of the three numbers in the vertical column. The largest possible value for the horizontal or vertical sum is
将五个数 1、4、7、10 和 13 分别放入五个方格中，使得横排三个数之和等于竖排三个数之和。水平或垂直和的最大可能值是
- A.20
- B.21
- C.22
- D.24
- E.30
正确答案 · Correct Answer
D
解析 · Solution
Solution 1
The largest sum occurs when 13 is placed in the center. This sum is . Note: Two other common sums, 18 and 21, are also possible.
Since the horizontal sum equals the vertical sum, twice this sum will be the sum of the five numbers plus the number in the center. When the center number is 13, the sum is the largest, The other four numbers are divided into two pairs with equal sums.
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