AMC 8 2005 Problem 3

AMC8 2005 年第 3 题

变换与对称★★☆☆☆

What is the minimum number of small squares that must be colored black so that a line of symmetry lies on the diagonal

\overline{BD}

of square ABCD ?

要使正方形

ABCD

的一条对称轴落在对角线

\overline{BD}

上，至少需要把多少个小正方形涂成黑色？

正确答案 · Correct Answer

解析 · Solution

Solution 1

Rotating square

ABCD

counterclockwise

45^\circ

so that the line of symmetry

BD

is a vertical line makes it easier to see that 4 squares need to be colored to match its corresponding square.

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