AMC8 1996
AMC8 1996 · Q14
AMC8 1996 · Q14. It mainly tests Basic counting (rules of product/sum), Casework.
Six different digits from the set $\{1, 2, 3, 4, 5, 6, 7, 8, 9\}$ 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 $\{1, 2, 3, 4, 5, 6, 7, 8, 9\}$ 中选取六个不同的数字放置在图示的方格中，使得垂直列的数字和为 23，水平行的数字和为 12。所用六个数字的和为
(A)
27
27
(B)
29
29
(C)
31
31
(D)
33
33
(E)
35
35
Answer
Correct choice: (B)
正确答案：（B）
Solution
The column must include 7,8,9 but adjusted; digits 1,2,3,6,8,9 sum to 29.
列必须包括 7,8,9 但需调整；数字 1,2,3,6,8,9 和为 29。
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