AMC8 1994
AMC8 1994 · Q24
AMC8 1994 · Q24. It mainly tests Basic counting (rules of product/sum), Symmetry.
A 2 by 2 square is divided into four 1 by 1 squares. Each of the small squares is to be painted either green or red. In how many different ways can the painting be accomplished so that no green square shares its top or right side with any red square? There may be as few as zero or as many as four small green squares.
一个2×2的正方形被分成四个1×1的小正方形。每个小正方形要么涂绿色要么涂红色。有多少种不同的涂色方式，使得没有绿色小方形与任何红色小方形共享其顶部或右侧？绿色小方形可以有0个到4个。
(A)
4
4
(B)
6
6
(C)
7
7
(D)
8
8
(E)
16
16
Answer
Correct choice: (B)
正确答案：（B）
Solution
Green squares force all above and right to be green. Possible configurations: all red; bottom-left green; bottom row green; left column green; bottom-left 2x2 green; all green. 6 ways.
绿色方形强制其上方和右侧全部为绿色。可能配置：全红；左下绿色；底行绿色；左列绿色；左下2×2绿色；全绿。6种方式。
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