Question

图中的展开图折成一个数字立方体。在立方体的每个顶点，都会有三个面相交。相交于同一个顶点的三个面上的数字，可能得到的最大和是多少？

The figure shown may be folded along the lines to form a number cube. Three faces come together at each corner of the cube. What is the largest sum of three numbers whose faces come together at a corner?

$11$

$12$

$13$

$14$

$15$

答案：D

知识点：展开图（立体几何）最优化

难度评级：920

解答：

折成立方体后，相对面不能在同一个顶点相遇。由展开图可判断相对面为 $1$ 与 $3$ 、 $2$ 与 $5$ 、 $4$ 与 $6$ 。

要让三个相邻面的和最大，就从每对相对面中取较大的数 $3$ 、 $5$ 和 $6$ 。它们可以在同一个顶点相遇，和为 $3 + 5 + 6 = 14$ 。

所以正确答案是 D。

When the net is folded, the pairs of opposite faces are $1$ and $3,$ $2$ and $5,$ and $4$ and $6.$ Three faces meeting at a corner must come one from each opposite pair.

To maximize the sum, take the larger number from each pair: $3,$ $5,$ and $6.$ These three faces do meet at a corner, and their sum is $3 + 5 + 6 = 14.$

Thus, the correct answer is D .

1989 AMC 8 第 20 题

答案：D

难度评级：920

解答：

其他年份的第 20 题