Difference between revisions of "2022 AMC 10A Problems/Problem 9"
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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> | |
| + | 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 21:28, 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?
![[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]](http://latex.artofproblemsolving.com/0/d/2/0d2429901955e7311077329c6e6b81a1939b686a.png)
