Difference between revisions of "2022 AMC 10A Problems/Problem 9"

(Created page with "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 d...")
 
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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?
 
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]
+
[img=https://latex.artofproblemsolving.com/texer/d/dzbefiwo.png?time=1668219982772][/img]
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]
 
 
 
 
<math>\textbf{(A) }120\qquad\textbf{(B) }270\qquad\textbf{(C) }360\qquad\textbf{(D) }540\qquad\textbf{(E) }720</math>
 
<math>\textbf{(A) }120\qquad\textbf{(B) }270\qquad\textbf{(C) }360\qquad\textbf{(D) }540\qquad\textbf{(E) }720</math>

Revision as of 22:26, 11 November 2022

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? [img=https://latex.artofproblemsolving.com/texer/d/dzbefiwo.png?time=1668219982772][/img] $\textbf{(A) }120\qquad\textbf{(B) }270\qquad\textbf{(C) }360\qquad\textbf{(D) }540\qquad\textbf{(E) }720$