Difference between revisions of "2017 AMC 12B Problems/Problem 13"
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==Problem 13== | ==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? | ||
| + | |||
| + | <asy> | ||
| + | size(100); | ||
| + | pair A, B, C, D, E, F; | ||
| + | A = (0,0); | ||
| + | B = (1,0); | ||
| + | C = (2,0); | ||
| + | D = rotate(60, A)*B; | ||
| + | E = B + D; | ||
| + | F = rotate(60, A)*C; | ||
| + | draw(Circle(A, 0.5)); | ||
| + | draw(Circle(B, 0.5)); | ||
| + | draw(Circle(C, 0.5)); | ||
| + | draw(Circle(D, 0.5)); | ||
| + | draw(Circle(E, 0.5)); | ||
| + | draw(Circle(F, 0.5)); | ||
| + | </asy> | ||
<math>\textbf{(A) } 6 \qquad \textbf{(B) } 8 \qquad \textbf{(C) } 9 \qquad \textbf{(D) } 12 \qquad \textbf{(E) } 15</math> | <math>\textbf{(A) } 6 \qquad \textbf{(B) } 8 \qquad \textbf{(C) } 9 \qquad \textbf{(D) } 12 \qquad \textbf{(E) } 15</math> | ||
Revision as of 21:35, 17 February 2017
Problem 13
In the figure below, 
of the 
disks are to be painted blue, 
are to be painted red, and 
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?
![[asy] size(100); pair A, B, C, D, E, F; A = (0,0); B = (1,0); C = (2,0); D = rotate(60, A)*B; E = B + D; F = rotate(60, A)*C; draw(Circle(A, 0.5)); draw(Circle(B, 0.5)); draw(Circle(C, 0.5)); draw(Circle(D, 0.5)); draw(Circle(E, 0.5)); draw(Circle(F, 0.5)); [/asy]](http://latex.artofproblemsolving.com/e/b/a/eba8bbf32167d960fbb94db72325cb3a2f89c234.png)
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 | |
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