Question

一个 $2$ 乘 $2$ 的正方形被分成四个 $1$ 乘 $1$ 的小正方形。每个小正方形要涂成绿色或红色。共有多少种不同涂法，使得没有任何绿色小正方形的上边或右边与红色小正方形相邻？绿色小正方形可以少到零个，也可以多到四个。

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.

$4$

$6$

$7$

$8$

$16$

答案：B

知识点：有限制的排列分类讨论

难度评级：1150

解答：

条件表示绿色方格不能在上方或右方紧邻红色方格，因此任何绿色方格都会迫使它上方和右方的方格也为绿色。绿色方格必须向右上角聚集。

合法涂法为：全红；只有右上角为绿；整行上排为绿；整列右排为绿；除左下角外全绿；全绿。共 $6$ 种。

所以正确答案是 B。

The rule says a green square cannot have a red square on its top or right side, so any green square forces the squares above and to its right to be green as well. The green squares must therefore cluster toward the top-right corner.

The valid colorings are: all four red; only the top-right green; the whole top row green; the whole right column green; all green except the bottom-left; and all four green. That is $6$ colorings.

Thus, the correct answer is B .

1994 AMC 8 第 24 题

答案：B

难度评级：1150

解答：

其他年份的第 24 题