Question

在一个 $3 \times 3$ 方格中，恰好涂黑九个单位正方形中的两个，可以形成多少种不同图案？通过翻转或旋转可以重合的图案不算不同。

How many different patterns can be made by shading exactly two of the nine unit squares in a $3 \times 3$ grid? Patterns that can be matched by flips and/or turns are not considered different.

$3$

$6$

$8$

$12$

$18$

答案：C

知识点：分类讨论对称性

难度评级：1470

解答：

先分类含有角格的图案：两个相邻角格、两个对角角格、角格与中心格、角格与相邻边中格、角格与较远边中格，共 $5$ 种。

不含角格的图案有：两个相邻边中格、两个相对边中格、一个边中格与中心格，共 $3$ 种。

总共有 $5 + 3 = 8$ 种不同图案。

所以正确答案是 C。

Classify the two shaded squares up to rotations and reflections. Patterns that include a corner: two adjacent corners (same edge), two diagonally opposite corners, corner with the center, corner with an adjacent edge-middle, and corner with a far edge-middle. That is $5$ patterns.

Patterns with no corner: two adjacent edge-middles, two opposite edge-middles, and an edge-middle with the center. That is $3$ more.

In total there are $5 + 3 = 8$ distinct patterns.

Thus, the correct answer is C .

1990 AMC 8 第 25 题

答案：C

难度评级：1470

解答：

其他年份的第 25 题