Math Gold Medalist

Lor

2022 AMC 12A 

Problem 7

A rectangle is partitioned into $5$ 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?

[asy] size(5.5cm); draw((0,0)--(0,2)--(2,2)--(2,0)--cycle); draw((2,0)--(8,0)--(8,2)--(2,2)--cycle); draw((8,0)--(12,0)--(12,2)--(8,2)--cycle); draw((0,2)--(6,2)--(6,4)--(0,4)--cycle); draw((6,2)--(12,2)--(12,4)--(6,4)--cycle); [/asy]

$\textbf{(A) }120\qquad\textbf{(B) }270\qquad\textbf{(C) }360\qquad\textbf{(D) }540\qquad\textbf{(E) }720$

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   Solution