2005 AMC 8 第 3 题
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所有题目均经美国数学协会（MAA）官方合法授权使用。
3.
最少还必须涂黑多少个小正方形，才能使对角线 成为正方形 的一条对称轴？
What is the minimum number of small squares that must be shaded so that a line of symmetry lies on the diagonal of square ?
小提示：
将已涂黑的小正方形关于对角线 反射
Reflect the shaded squares across diagonal .
大提示：
只有没有对应反射涂黑方格的已涂黑方格需要配对
Only shaded squares without a matching reflected square need to be paired.
解答：
要使对角线 成为对称轴，对角线外每个已涂黑小正方形都必须在对角线另一侧有一个对应的反射涂黑小正方形。
有 个已涂黑小正方形的反射位置尚未涂黑，所以还必须涂黑 个小正方形。
所以正确答案是 D。
For diagonal to be a line of symmetry, every shaded square off the diagonal must have a matching reflected shaded square on the other side of the diagonal.
There are shaded squares whose reflected partners are not shaded, so additional small squares must be shaded.
Thus, D is the correct answer.
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