AMC8 2026

AMC8 2026 · Q15

AMC8 2026 · Q15. It mainly tests 3D geometry (volume), 3D geometry (surface area).

Elijah has a large collection of identical wooden cubes which are white on 4 faces and gray on 2 faces that share an edge. He glues some cubes together face-to-face. The figure below shows 2 cubes being glued together, leaving 3 gray faces visible. What is the fewest number of cubes that he could glue together to ensure that no gray faces are visible, no matter how he rotates the figure?

Elijah 有一大批相同的木制立方体，这些立方体有 4 个面为白色，2 个面为灰色，且这两个灰色面共用一条边。他将一些立方体面与面地粘在一起。下图显示了两个立方体被粘在一起，露出了 3 个灰色面。要确保无论如何旋转图形，都看不到灰色面，他最少需要粘多少个立方体？

(A) 4 4

(B) 6 6

(D) 9 9

(E) 27 27

Answer

Correct choice: (A)

正确答案：（A）

Solution

We can have $4$ cubes with all their gray faces facing each other, and that will make no gray faces visible. Therefore, our answer is $\boxed{\textbf{(A)}\ 4}$.

我们可以用 4 个立方体，使所有灰色面都相互朝向，这样就不会有灰色面可见。因此，答案是 $\boxed{\textbf{(A)}\ 4}$。

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