AMC8 1990
AMC8 1990 · Q25
AMC8 1990 · Q25. It mainly tests Basic counting (rules of product/sum), Counting with symmetry / Burnside (rare).
How many difference patterns can be made by shading exactly two of the nine squares? Patterns that can be matched by flips and/or turns are not considered different.
在九个方格中恰好涂黑两个，能形成多少种不同的图案？可以通过翻转和/或旋转匹配的图案不视为不同。
(A)
3
3
(B)
6
6
(C)
8
8
(D)
12
12
(E)
18
18
Answer
Correct choice: (C)
正确答案：（C）
Solution
Answer (C): There are $8$. Be systematic. You can begin with the five cases that have one corner square. Then consider the other three cases that do not have a corner square.
答案（C）：共有 $8$ 种。要有条理地分类。可以先从包含一个角落方格的 5 种情况开始，再考虑另外 3 种不包含角落方格的情况。
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