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Difference between revisions of "2017 AMC 12B Problems/Problem 13"

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==Problem 13==
 
In the figure below, <math>3</math> of the <math>6</math> disks are to be painted blue, <math>2</math> are to be painted red, and <math>1</math> is to be painted green. Two paintings that can be obtained from one another by a rotation or a reflection of the entire figure are considered the same. How many different paintings are possible?
 
In the figure below, <math>3</math> of the <math>6</math> disks are to be painted blue, <math>2</math> are to be painted red, and <math>1</math> is to be painted green. Two paintings that can be obtained from one another by a rotation or a reflection of the entire figure are considered the same. How many different paintings are possible?
  
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[asy]
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<math>\textbf{(A) } 6 \qquad \textbf{(B) } 8 \qquad \textbf{(C) } 9 \qquad \textbf{(D) } 12 \qquad \textbf{(E) } 15</math>
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size(100);
 
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pair A, B, C, D, E, F;
 
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A = (0,0);
 
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B = (1,0);
 
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C = (2,0);
 
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D = rotate(60, A)*B;
 
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E = B + D;
 
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F = rotate(60, A)*C;
 
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draw(Circle(A, 0.5));
 
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draw(Circle(B, 0.5));
 
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draw(Circle(C, 0.5));
 
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draw(Circle(D, 0.5));
 
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draw(Circle(E, 0.5));
 
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draw(Circle(F, 0.5));
 
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[/asy]
 
  
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<math>\textbf{(A) } 6 \qquad \textbf{(B) } 8 \qquad \textbf{(C) } 9 \qquad \textbf{(D) } 12 \qquad \textbf{(E) } 15</math>
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==Solution==
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WORK IN PROGRESS
  
 
==See Also==
 
==See Also==
 
{{AMC12 box|year=2017|ab=B|num-b=12|num-a=14}}
 
{{AMC12 box|year=2017|ab=B|num-b=12|num-a=14}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Revision as of 21:24, 17 February 2017

Problem 13

In the figure below, $3$ of the $6$ disks are to be painted blue, $2$ are to be painted red, and $1$ is to be painted green. Two paintings that can be obtained from one another by a rotation or a reflection of the entire figure are considered the same. How many different paintings are possible?

$\textbf{(A) } 6 \qquad \textbf{(B) } 8 \qquad \textbf{(C) } 9 \qquad \textbf{(D) } 12 \qquad \textbf{(E) } 15$

Solution

WORK IN PROGRESS

See Also

2017 AMC 12B (Problems • Answer Key • Resources)
Preceded by
Problem 12 		Followed by
Problem 14
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AMC 12 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png

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