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 (R), white (W), green (G), brown (B), aqua (A), and purple (P). Three views of the cube are shown below. What is the color of the face opposite the aqua face? | + | 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? |
[[File:2019AMC8Prob12.png]] | [[File:2019AMC8Prob12.png]] | ||
| − | |||
==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 2)<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 | + | <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 |
==Solution 2== | ==Solution 2== | ||
| − | Looking closely we can see that all faces | + | 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>. |
| + | 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== |
{{AMC8 box|year=2019|num-b=11|num-a=13}} | {{AMC8 box|year=2019|num-b=11|num-a=13}} | ||
Only two of the cubes are required to solve the problem. | 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.
