Difference between revisions of "2019 AMC 8 Problems/Problem 12"
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==Problem== | ==Problem== | ||
| + | The faces of a cube are painted in six different colors: red <math>(R)</math>, white <math>(W)</math>, green <math>(G)</math>, brown <math>(B)</math>, aqua <math>(A)</math>, and purple <math>(P)</math>. Three views of the cube are shown below. What is the color of the face opposite the aqua face? | ||
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| + | [[File:2019AMC8Prob12.png]] | ||
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==Solution 1== | ==Solution 1== | ||
| + | <math>B</math> is on the top, and <math>R</math> is on the side, and <math>G</math> is on the right side. That means that (image <math>2</math>) <math>W</math> is on the left side. From the third image, you know that <math>P</math> must be on the bottom since <math>G</math> is sideways. That leaves us with the back, so the back must be <math>A</math>. The front is opposite of the back, so the answer is <math>\boxed{\textbf{(A)}\ R}</math>.~heeeeeeeheeeee | ||
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==Solution 2== | ==Solution 2== | ||
| + | Looking closely we can see that all faces are connected with <math>R</math> except for <math>A</math>. Thus the answer is <math>\boxed{\textbf{(A)}\ R}</math>. | ||
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| + | It is A, just draw it out! | ||
| + | ~phoenixfire | ||
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| + | ==Solution 3== | ||
| + | Associated video - https://www.youtube.com/watch?v=K5vaX_EzjEM | ||
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| + | Video Solution- https://youtu.be/Lw8fSbX_8FU ( Also explains problems 11-20) | ||
| + | |||
| + | ==See also== | ||
| + | {{AMC8 box|year=2019|num-b=11|num-a=13}} | ||
| + | Only two of the cubes are required to solve the problem. | ||
Revision as of 13:23, 31 October 2020
Problem
The faces of a cube are painted in six different colors: red 
, white 
, green 
, brown 
, aqua 
, and purple 
. Three views of the cube are shown below. What is the color of the face opposite the aqua face?
Solution 1
is on the top, and 
is on the side, and 
is on the right side. That means that (image 
) 
is on the left side. From the third image, you know that 
must be on the bottom since is sideways. That leaves us with the back, so the back must be 
. The front is opposite of the back, so the answer is 
.~heeeeeeeheeeee
Solution 2
Looking closely we can see that all faces are connected with except for . Thus the answer is .
It is A, just draw it out! ~phoenixfire
Solution 3
Associated video - https://www.youtube.com/watch?v=K5vaX_EzjEM
Video Solution- https://youtu.be/Lw8fSbX_8FU ( Also explains problems 11-20)
See also
| 2019 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 11 |
Followed by Problem 13 | |
| 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 AJHSME/AMC 8 Problems and Solutions | ||
Only two of the cubes are required to solve the problem.
