2022 AMC 12A 第 7 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。
7.
一个长方形如图被分成 个区域。每个区域要涂成一种纯色，可选颜色为红、橙、黄、蓝、绿。相接触的区域必须涂成不同颜色，颜色可以重复使用。共有多少种不同的涂色方法？
A rectangle is partitioned into regions as shown. Each region is to be painted a solid color - red, orange, yellow, blue, or green - so that regions that touch are painted different colors, and colors can be used more than once. How many different colorings are possible?
小提示：
先给与最多其他区域相邻的区域涂色
Color the region that borders the most others first
大提示：
有一个区域与另外四个区域都相邻；其余每个区域都必须避开两个已经使用的颜色
One region touches all four others; each remaining region must avoid two already-used colors
解答：
底部中间的区域与其他四个区域都共边。先给它涂色，有 种方法。
左上区域与它相邻，有 种选择。其余三个区域各与两个已经涂好的区域相邻，而这两个区域颜色不同，所以各有 种选择。
总数为 。
因此，正确答案是 D。
The bottom-middle region shares a border with all four other regions. Color it first in ways.
The top-left region borders it, giving choices. Each of the three remaining regions borders exactly two already-colored regions, which have different colors, leaving choices apiece.
The total is
Thus, the correct answer is D.
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