AMC 8 1996 Problem 14
AMC8 1996 年第 14 题
特殊数与不定方程★★★☆☆
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 23 and the sum of the entries in the horizontal row is 12. The sum of the six digits used is
从集合 中选取六个不同的数字填入图中所示的方格，使得竖列各项之和为 23，横行各项之和为 12。所用六个数字之和为
- A.27
- B.29
- C.31
- D.33
- E.35
正确答案 · Correct Answer
B
解析 · Solution
Solution 1
Looking at the vertical column, the three numbers sum to 23. If we make the numbers on either end 9 and 8 in some order, the middle number will be 6. This is the minimum for the intersection.
Looking at the horizontal row, the four numbers sum to 12. If we minimize the three numbers on the right to 123, the first number has a maximum value of 6. This is the maximum for the intersection
Thus, the minimum of the intersection is 6, and the maximum of the intersection is 6. This means the intersection must be 6, and the other numbers must be 9 and 8 in the column, and 123 in the row. The sum of all the numbers is .
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