AMC 8 1990 Problem 11
AMC8 1990 年第 11 题
奇偶性★★★☆☆
The numbers on the faces of this cube are consecutive whole numbers. The sum of the two numbers on each of the three pairs of opposite faces are equal. The sum of the six numbers on this cube is
此正方体面上的数字是连续的正整数。三组相对面上每组的两个数字之和相等。正方体上六个数字之和为
- A.75
- B.76
- C.78
- D.80
- E.81
正确答案 · Correct Answer
E
解析 · Solution
Solution 1
Since 11 and 15 are among the 6 consecutive whole numbers, the numbers must be either or .
If the numbers were , each pair of opposite faces would sum to . But 11 would be opposite 14, which is not the case on this cube.
Therefore, the numbers are , which works if 16, 13, and 12 are placed opposite 11, 14, and 15 respectively. In this case, the sum is 11+12+13+14+15+16=81.
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